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1
Weber, Harald. "Group rings and twisted group rings for a series of p-groups." [S.l. : s.n.], 2003. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10761310.
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Wilson, James B. "Group decompositions, Jordan algebras, and algorithms for p-groups /." Connect to title online (Scholars' Bank) Connect to title online (ProQuest), 2008. http://hdl.handle.net/1794/8302.
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Thesis (Ph. D.)--University of Oregon, 2008.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 121-125). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.
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Wilson, James B. 1980. "Group decompositions, Jordan algebras, and algorithms for p-groups." Thesis, University of Oregon, 2008. http://hdl.handle.net/1794/8302.
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viii, 125 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.Finite p -groups are studied using bilinear methods which lead to using nonassociative rings. There are three main results, two which apply only to p -groups and the third which applies to all groups. First, for finite p -groups P of class 2 and exponent p the following are invariants of fully refined central decompositions of P : the number of members in the decomposition, the multiset of orders of the members, and the multiset of orders of their centers. Unlike for direct product decompositions, Aut P is not always transitive on the set of fully refined central decompositions, and the number of orbits can in fact be any positive integer. The proofs use the standard semi-simple and radical structure of Jordan algebras. These algebras also produce useful criteria for a p -group to be centrally indecomposable. In the second result, an algorithm is given to find a fully refined central decomposition of a finite p -group of class 2. The number of algebraic operations used by the algorithm is bounded by a polynomial in the log of the size of the group. The algorithm uses a Las Vegas probabilistic algorithm to compute the structure of a finite ring and the Las Vegas MeatAxe is also used. However, when p is small, the probabilistic methods can be replaced by deterministic polynomial-time algorithms. The final result is a polynomial time algorithm which, given a group of permutations, matrices, or a polycyclic presentation; returns a Remak decomposition of the group: a fully refined direct decomposition. The method uses group varieties to reduce to the case of p -groups of class 2. Bilinear and ring theory methods are employed there to complete the process.
Adviser: William M. Kantor
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Blackburn, Simon R. "Group enumeration." Thesis, University of Oxford, 1992. http://ora.ox.ac.uk/objects/uuid:caac5ed0-44e3-4bec-a97e-59e11ea268af.
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The thesis centres around two problems in the enumeration of p-groups. Define fφ(pm) to be the number of (isomorphism classes of) groups of order pm in an isoclinism class φ. We give bounds for this function as φ is fixed and m varies and as m is fixed and φ varies. In the course of obtaining these bounds, we prove the following result. We say a group is reduced if it has no non-trivial abelian direct factors. Then the rank of the centre Z(P) and the rank of the derived factor group P|P' of a reduced p-group P are bounded in terms of the orders of P|Z(P)P' and P'∩Z(P). A long standing conjecture of Charles C. Sims states that the number of groups of order pm isp2andfrasl;27m3+O(m2). (1) We show that the number of groups of nilpotency class at most 3 and order pm satisfies (1). We prove a similar result concerning the number of graded Lie rings of order pm generated by their first grading.
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Welch, Amanda Renee. "Characterizing Zero Divisors of Group Rings." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/52949.
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The Atiyah Conjecture originates from a paper written 40 years ago by Sir Michael Atiyah,
a famous mathematician and Fields medalist. Since publication of the paper, mathematicians
have been working to solve many questions related to the conjecture, but it is still open.
The conjecture is about certain topological invariants attached to a group G. There are
examples showing that the conjecture does not hold in general. These examples involve
something like the lamplighter group. We are interested in
looking at examples where this is not the case. We are interested in the specific case where
G is a finitely generated group in which the Pr'ufer group can be embedded as the center.
The Pr'ufer group is a p-group for some prime p and its finite subgroups have unbounded
order, in particular the finite subgroups of G will have unbounded order.
To understand whether any form of the Atiyah conjecture is true for G, it will first help to
determine whether the group ring kG of the group G has a classical ring of quotients for
some field k. To determine this we will need to know the zero divisors for the group ring
kG. Our investigations will be divided into two cases, namely when the characteristic of the
field k is the same as the prime p for the Pr'ufer group and when it is different.Master of Science
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Johansson, Isak. "Themod p Cohomology of the ProjectiveUnitary Group." Thesis, KTH, Matematik (Avd.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-229678.
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We begin with an introduction to spectral sequences, in particular, we present how a spectral sequence can arise from an exact couple, state and construct the Serre spectral sequence, mention some of the properties of the mod p cohomology and state the dual Eilenberg-Moore spectral sequence. Fiber bundles, together with the concept of pullback bundles, principal bundles, classifying spaces and Chern classes are also discussed to lay a foundation for our results. We compute the mod p cohomology of the projective unitary group. Finally, we compute the mod 3 cohomology of the classifying space of the projective unitary group of order 3.Denna uppsats inleds med en introduktion till spektralsekvenser. Vi visar hur spektrala sekvenser uppkommer från exakta par. Vidare presenteras Serres spektralsekvens, egenskaper hos mod p kohomologin och den duala versionen av Eilenberg-Moores spektralsekvens. Fiberknippen, huvudknippen, klassificerande rum och Cherns klasser diskuteras även och ligger till grund för våra resultat. Vi beräknar mod p kohomologin av den projektiva unitära gruppen. Slutligen beräknar vi mod 3 kohomologin av det klassificerande rummet av den projektiva unitära gruppen av ordning 3.
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Schoemann, Claudia. "Représentations unitaires de U(5) p-adique." Thesis, Montpellier 2, 2014. http://www.theses.fr/2014MON20101.
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Nous étudions les représentations complexes, induites par l'induction parabolique, du groupe U(5), défini sur un corps local non-archimedean de caractéristique 0. C'est Qp ou une extension finie de Qp .On parle des 'corps p-adiques'. Soit F un corps p-adique. Soit E : F une extension de corps de degré 2. Soit Gal(E : F ) = {id, σ}le groupe de Galois. On écrit σ(x) = overline{x} forall x ∈ E. Soit | |p la norme p-adique de E. Soient E* = E {0} et E 1 = {x ∈ E | xoverline{x}= 1} .U (5) a trois sous-groupes paraboliques propres. Soit P0 le sous-groupe parabolique minimal et soientP1 et P2 les deux sous-groupes paraboliques maximaux. Soient M0 , M1 et M2 les sous-groupes de Levi standards et soient N0 , N1 et N2 des sous-groupes unipotents de U (5). On a la décomposition de Levi Pi = Mi Ni , i ∈{0, 1, 2} .M0 = E* × E* × E 1 est le sous-groupe de Levi minimal, M1 = GL(2, E) × E 1 et M2 = E* × U(3) sont les sous-groupes de Levi maximaux.On considère les représentations des sous-groupes de Levi, et on les étend trivialement au sous-groupes unipotents pour obtenir des représentations des sous-groupes paraboliques. On exécute une procédure appelée 'l'induction parabolique' pour obtenir les représentations de U (5). Nous considérons les représentations de M0 , puis les représentations non-cuspidales, induites à partir de M1 et M2 . Cela veut dire que la représentation du facteur GL(2, E) de M1 est un sous-quotient propre d'une représentation induite de E* × E* à GL(2, E). La représentation du facteur U (3) de M2 est un sous-quotient propre d'une représentation induite de E* × E 1 à U(3). Un exemple pour M1 est | det |α χ(det) StGL2 * λ' , où α ∈ R, χ est un caractère unitaire de E* , StGL2 est la représentation Steinberg de GL(2, E) et λ' est un caractère de E 1 . Un exemple pour M2 est| |α χ λ (det) StU (3) , où α ∈ R, χ est un caractère unitaire de E* , λ' est un caractère unitaire de E 1et StU (3) est la représentation Steinberg de U(3). On remarque que λ' est unitaire.Ensuite on considère les représentations cuspidales de M1 .On détermine les droites et les points de réductibilité des représentations de U(5) et on détermine les sous-quotients irréductibles. Ensuite, sauf quelque cas particuliers, on détermine le dual unitaire de U(5)par rapport au quotients de Langlands. Les représentations complexes, paraboliquement induites, de U(3) sur un corps p-adique sont classifiées par Charles David Keys dans [Key84], les représentations complexes, paraboliquement induites, de U(4)sur un corps p-adique sont classifiées par Kazuko Konno dans [Kon01]We study the parabolically induced complex representations of the unitary group in 5 variables - U(5)- defined over a non-archimedean local field of characteristic 0. This is Qp or a finite extension of Qp ,where p is a prime number. We speak of a 'p-adic field'.Let F be a p-adic field. Let E : F be a field extension of degree two. Let Gal(E : F ) = {id, σ}. We write σ(x) = overline{x} forall x ∈ E. Let | |p denote the p-adic norm on E. Let E* := E {0} and let E 1 := {x ∈ E | x overline{x} = 1} .U(5) has three proper parabolic subgroups. Let P0 denote the minimal parabolic subgroup and P1 andP2 the two maximal parabolic subgroups. Let M0 , M1 and M2 denote the standard Levi subgroups and let N0 , N1and N2 denote unipotent subgroups of U(5). One has the Levi decomposition Pi = Mi Ni , i ∈ {0, 1, 2} .M0 = E* × E* × E 1 is the minimal Levi subgroup, M1 = GL(2, E) × E 1 and M2 = E* × U (3) are the two maximal parabolic subgroups.We consider representations of the Levi subgroups and extend them trivially to the unipotent subgroups toobtain representations of the parabolic groups. One now performs a procedure called 'parabolic induction'to obtain representations of U (5).We consider representations of M0 , further we consider non-cuspidal, not fully-induced representationsof M1 and M2 . For M1 this means that the representation of the GL(2, E)− part is a proper subquotientof a representation induced from E* × E* to GL(2, E). For M2 this means that the representation of theU (3)− part of M2 is a proper subquotient of a representation induced from E* × E 1 to U (3).As an example for M1 , take | det |α χ(det) StGL2 * λ' , where α ∈ R, χ is a unitary character of E* , StGL2 is the Steinberg representation of GL(2, E) and λ' is a character of E 1 . As an example forM2 , take | |α χ λ' (det) StU (3) , where α ∈ R, χ is a unitary character of E* , λ' is a character of E 1 andStU (3) is the Steinberg representation of U (3). Note that λ' is unitary.Further we consider the cuspidal representations of M1 .We determine the points and lines of reducibility of the representations of U(5), and we determinethe irreducible subquotients. Further, except several particular cases, we determine the unitary dual ofU(5) in terms of Langlands-quotients.The parabolically induced complex representations of U(3) over a p-adic field have been classied byCharles David Keys in [Key84], the parabolically induced complex representations of U(4) over a p-adicfield have been classied by Kazuko Konno in [Kon01].An aim of further study is the classication of the induced complex representations of unitary groupsof higher rank, like U (6) or U (7). The structure of the Levi subgroups of U (6) resembles the structureof the Levi subgroups of U (4), the structure of the Levi groups of U (7) resembles those of U (3) and ofU (5).Another aim is the classication of the parabolically induced complex representatioins of U (n) over ap-adic field for arbitrary n. Especially one would like to determine the irreducible unitary representations
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Smith, Duncan Alexander Mathematics UNSW. "The Families with Period 1 of 2-groups of Coclass 3." Awarded by:University of New South Wales. Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17792.
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The 2-groups of coclass 1 are widely known and James (in 1975) looked at the 2-groups of coclass 2. Development of the p-group generation algorithm implemented by O'Brien at ANU enabled group presentations to be provided for the 2-groups of coclass 3 by Newman and O'Brien for groups of order up to 223. Newman and O'Brien (in 1999) conjectured the number of descendants of 2n for all n. They introduced the concept of a family, with each family related to a different pro-p-group and the concept of a sporadic p-group, a p-group external to any family. They found 1782 sporadic 2-groups with order at most 214. The 70 families of 2-groups of coclass 3 can be further split according to their period, a measure of the repetitive structure of the families. Newman and O'Brien conjectured that these families had periods of 1, 2 or 4. This thesis examines the 2-groups of coclass 3 contained in families with period 1 and shows that the number of descendants conjectured by Newman and O'Brien is correct. Furthermore the presentation of all groups contained in period 1 families is provided and shown to be correct.
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Crestani, Eleonora. "Monotone 2-Groups." Doctoral thesis, Università degli studi di Padova, 2009. http://hdl.handle.net/11577/3426499.
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The generation problems are very interesting in the theory of finite groups. These problems can often be reduced to problems on the generators of p-groups. This has led to an increasing interest on the problems of generation in p-groups and on the study of classes of p-groups in which generators satisfy some precise conditions.
In particular, it is very interesting the class of finite p-groups G with the property that the rank of G is equal to the number of generators of G (i.e. the number of generators of every subgroup of G is smaller than or equal to the number of generators of G). For instance, the abelian, the modular and the powerful p-groups belong to this class. Also the monotone p-groups lie in this class. We recall here the definition of monotone p-groups.
Definition: Let G be a group. We denote with d(G) the number of generators of G.
A p-group G is monotone if for every H and K subgroups of G with H contained in K, we have that d(H) is smaller than or equal to d(K).
The class of monotone p-groups was introduced by A. Mann during the 1985 Saint Andrews Conference. In the paper " The number of generators of finite p-groups" published in 2005, Mann studies the monotone p-groups and classifies the monotone p-groups for p odd.
When p=2, Mann does not classify the monotone 2-groups, but he gives some remarkable properties. For instance, he proves that a 2-group G is monotone if and only if the 2-generated subgroups of G are metacyclic.
In this thesis, the monotone 2-groups are studied and completely determined.I problemi di generazione sono problemi estremamente interessanti nella teoria dei gruppi finiti. Tali problemi spesso si riducono a problemi sui generatori di p-gruppi. Questo ha portato ad un sempre maggiore interesse per i problemi di generazione nei p-gruppi e allo studio di classi di p-gruppi finiti in cui i generatori del gruppo e dei sottogruppi soddisfano alcune precise condizioni. Di particolare interesse é la classe dei p-gruppi finiti G tali che il numero di generatori di ogni sottogruppo H di G è minore o uguale del numero di generatori di G. Esempi di p-gruppi appartenenti a questa classe sono i p-gruppi abeliani, i p-gruppi modulari e i p-gruppi powerful. Soddisfano tale proprietà anche i p-gruppi monotoni. Per questi ultimi ricordiamo la definizione. Definizione. Dato G un gruppo, sia d(G) il numero di generatori di G. Un p-gruppo G si dice monotono se per ogni H e K sottogruppi di G con H contenuto in K, si ha che d(H) è minore o uguale a d(K). I p-gruppi monotoni sono stati introdotti da A. Mann durante una conferenza tenutasi a Saint Andrews nel 1985. Lo stesso autore, in "The number of generators of finite p-groups", lavoro pubblicato nel 2005, studia i p-gruppi monotoni e li classifica per p dispari. Del caso p=2, non viene data alcuna classificazione ma vengono date alcune proprietà interessanti. Ad esempio, Mann dimostra che un 2-gruppo G è monotono se e solo se i sottogruppi 2-generati di G sono metaciclici. In questa tesi vengono studiati e classificati completamente i 2-gruppi monotoni.
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Schwingel, Ruth. "Two matrix group algorithms with applications to computing the automorphism group of a finite p-group." Thesis, Queen Mary, University of London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313397.
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Wald, Christian. "A p-adic quantum group and the quantized p-adic upper half plane." Doctoral thesis, Humboldt-Universität zu Berlin, 2017. http://dx.doi.org/10.18452/18201.
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Eine Quantengruppe ist eine nichtkommutative und nichtkokommutative Hopfalgebra. In dieser Arbeit konstruieren wir eine Deformation der lokalkonvexen Hopfalgebra der lokalanalytischen Funktionen auf GL(2,O), wobei O hier der Bewertungsring einer endlichen Erweiterung der p-adischen Zahlen ist. Wir zeigen, dass diese Deformation eine nichtkommutative, nichtkokommutative lokalkonvexe Hopfalgebra, also eine p-adische Quantengruppe, ist. Unser Hauptresultat ist, dass das starke Dual dieser Deformation eine Fréchet-Stein Algebra ist. Dies bedeutet, dass das starke Dual ein projektiver Limes von noetherschen Banachalgebren unter rechtsflachen Übergangsabbildungen ist. Im kommutativen Fall wurde dies von P. Schneider und J. Teitelbaum gezeigt. Unser Beweis im nichtkommutativen Fall benutzt Ideen von M. Emerton, der einen alternativen Beweis im kommutativen Fall gefunden hat. Für unseren Beweis beschreiben wir gewisse Vervollständigungen der quanten-einhüllenden Algebra und benutzen die Technik der partiell dividierten Potenzen. Eine wichtige Klasse lokalanalytischer Darstellungen von GL(2,K) wird mithilfe globaler Schnitte von Linienbündeln auf der p-adischen oberen Halbebene konstruiert. Wir konstruieren ein nichtkommutatives Analogon der p-adischen oberen Halbebene, von dem wir erwarten, dass es interessante Darstellungen unserer p-adischen Quantengruppe induziert. Die wichtigsten Hilfsmittel der Konstruktion sind die Maninsche Quantenebene, der Bruhat-Tits Baum für PGL(2,K) und die Theorie der algebraischen Mikrolokalisierung.A quantum group is a noncommutative noncocommutative Hopf algebra. In this thesis we deform the locally convex Hopf algebra of locally analytic functions on GL(2,O), where O is the valuation ring of a finite extension of the p-adic numbers. We show that this deformation is a noncommutative noncocommutative locally convex Hopf algebra, i.e. a p-adic quantum group. Our main result is that the strong dual of our deformation is a Fréchet Stein algebra, i.e. a projective limit of Noetherian Banach algebras with right flat transition maps. This was shown in the commutative case by P. Schneider and J. Teitelbaum. For our proof in the noncommutative case we use ideas of M. Emerton, who gave an alternative proof of the Fréchet Stein property in the commutative case. For the proof we describe completions of the quantum enveloping algebra and use partial divided powers. An important class of locally analytic representations of GL(2,K) is constructed from global sections of line bundles on the p-adic upper half plane. We construct a noncommutative analogue of an affine version of the p-adic upper half plane which we expect to give rise to interesting representations of our p-adic quantum group. We construct this space by using the Manin quantum plane, the Bruhat-Tits tree for PGL(2,K) and the theory of algebraic microlocalization.
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TOSSICI, DAJANO. "Group schemes of order p^2 and extension of Z/p^2Z-torsors." Doctoral thesis, Università di Roma Tre, 2008. http://hdl.handle.net/10281/20961.
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In this work we study finite group schemes over a discrete valuation ring of unequal characteristic which are isomorphic to the group scheme of p^2-roots of unity, where p is the characteristic of the residue field of R, on the generic fiber. And we apply this to the study of the degeneration, from caracteristic p to caracteristic 0, of torsors under the cyclic group of order p^2.
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Withrow, Camron Michael. "Left Orderable Residually Finite p-groups." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/24782.
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Let p and q be distinct primes, and G an elementary amenable group that is a residually
finite p-group and a residually finite q-group. We conjecture that such groups G are left
orderable. In this paper we show some results which came as attempts to prove this conjecture. In particular we give a condition under which split extensions of residually finite
p-groups are again residually finite p-groups. We also give an example which shows that
even for elementary amenable groups, it is not sufficient for biorderablity that the group be
a residually finite p-group and a residually finite q-group.Master of Science
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Sewell, Cynthia M. (Cynthia Marie). "The Eulerian Functions of Cyclic Groups, Dihedral Groups, and P-Groups." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc500684/.
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In 1935, Philip Hall developed a formula for finding the number of ways of generating the group of symmetries of the icosahedron from a given number of its elements. In doing so, he defined a generalized Eulerian function. This thesis uses Hall's generalized Eulerian function to calculate generalized Eulerian functions for specific groups, namely: cyclic groups, dihedral groups, and p- groups.
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Eisele, Florian [Verfasser]. "Group rings over the p-Adic integers / Florian Eisele." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2012. http://d-nb.info/1022616773/34.
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Croome, Sarah B. "p-Group Codegree Sets and Nilpotence Class." Kent State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1554462855786456.
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Feldmann, Mark [Verfasser], and Peter [Akademischer Betreuer] Schneider. "p-adic Weil group representations / Mark Feldmann ; Betreuer: Peter Schneider." Münster : Universitäts- und Landesbibliothek Münster, 2018. http://d-nb.info/1168324815/34.
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Barker, Nathan. "Topics in algebra : the Higman-Thompson group G b2 s, b1 s and Beauville p-groups." Thesis, University of Newcastle upon Tyne, 2014. http://hdl.handle.net/10443/2648.
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This thesis consists of two parts. Part I of this thesis is concerned with the Higman-Thompson group G2,1. We review and apply Definitions, Lemmas and Theorems described in a series of lectures delivered by Graham Higman during a visit to the Australian National University from July 1973 to October 1973 on a family of finitely presented infinite groups Gn,r for n 2 and r 1. This thesis will concentrate on the group G2,1 (otherwise know as Thompson’s group V). We give a brief account of the history of the Higman-Thompson group G2,1, we clarify the proof of the conjugacy problem for elements in quasi-normal form and we prove that the power conjugacy problem for the group G2,1 is decidable. Part II of this thesis concentrates on the existence and structure of mixed and unmixed Beauville p-groups, for p a prime. We start by exhibiting the first explicit family of mixed Beauville 2-groups and find the corresponding surfaces. We follow this up by exploring the method that was used to construct the family; this leads to further ramification structures for finite p-groups giving rise to surfaces isogenous to a higher product of curves. We finish by classifying the non-abelian Beauville pgroups of order p3, p4 and provide partial results for p-groups of order p5 and p6. We also construct the smallest Beauville p-groups for each prime p.
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Djabri, Zafer M. "P-descent on elliptic curves over number fields." Thesis, University of Kent, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.310161.
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Ives-Allison, Nicole D. "P stones and provos : group violence in Northern Ireland and Chicago." Thesis, University of St Andrews, 2015. http://hdl.handle.net/10023/6925.
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Although the government of the United States of America was established to protect the rights to life, liberty and the pursuit of happiness among all American citizens, this thesis argues intractable gang violence in inner-city Chicago has persistently denied these rights, in turn undermining fundamental (and foundational) American political values. Thus, gang violence can be argued to represent a threat to both civil order and state legitimacy. Yet, where comparable (and generally lower) levels of community-level violence in Northern Ireland garnered the sustained attention and direct involvement of the United Kingdom's central government, the challenge posed by gang violence has been unappreciated, if not ignored, by the American federal government. In order to mobilise the political commitment and resources needed to find a durable resolution to Chicago's long and often anarchic 'uncivil war', it is first necessary to politicise the problem and its origins. Contributing to this politicisation, this thesis explains why gang violence in Chicago has been unable to capture the political imagination of the American government in a way akin to paramilitary (specifically republican) violence in Northern Ireland. Secondly, it explains how the depoliticisation of gang violence has negatively affected response, encouraging the continued application of inadequate and largely ineffective response strategies. Finally, it makes the case that, while radical, a conditional agreement-centric peace process loosely modelled on that employed in Northern Ireland might offer the most effective strategy for restoring the sense of peace and security to inner-city Chicago lost over half a century ago.
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Vaintrob, Dmitry. "Mirror symmetry and the K theory of a p-adic group." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104578.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 59-61).
Let G be a split, semisimple p-adic group. We construct a derived localization functor Loc : ... from the compactified category of [BK2] associated to G to the category of equivariant sheaves on the Bruhat-Tits building whose stalks have finite-multiplicity isotypic components as representations of the stabilizer. Our construction is motivated by the "coherent-constructible correspondence" functor in toric mirror symmetry and a construction of [CCC]. We show that Loc has a number of useful properties, including the fact that the sections ... compactifying the finitely-generated representation V. We also construct a depth by Dmitry A. Vaintrob.
Ph. D.
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Decker, Erin. "On the construction of groups with prescribed properties." Diss., Online access via UMI:, 2008.
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Chinner, Trinity. "Elliptic Tori in p-adic Orthogonal Groups." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/42759.
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In this thesis, we classify up to conjugacy the maximal elliptic toral subgroups of all
special orthogonal groups SO(V), where (q,V) is a 4-dimensional quadratic space
over a non-archimedean local field of odd residual characteristic. Our parameterization blends the abstract theory of Morris with a generalization of the practical work
performed by Kim and Yu for Sp(4). Moreover, we compute an explicit Witt basis
for each such torus, thereby enabling its concrete realization as a set of matrices embedded into the group. This work can be used explicitly to construct supercuspidal
representations of SO(V).
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Hauseux, Julien. "Extensions entre séries principales p-adiques et modulo p d'un groupe réductif p-adique déployé." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112411/document.
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Cette thèse est une contribution à l'étude des représentations p-adiques (c'est-à-dire continues unitaires sur des espaces de Banach p-adiques) et modulo p (c'est-à-dire lisses sur un corps fini de caractéristique p) d'un groupe réductif p-adique déployé G.Nous déterminons les extensions entre séries principales p-adiques et modulo p de G Pour cela, nous calculons le delta-foncteur H•OrdB des parties ordinaires dérivées d'Emerton relatif à un sous-groupe de Borel sur une série principale en utilisant une filtration de Bruhat.Nous déterminons également les extensions d'une série principale par une représentation ordinaire (c'est-à-dire obtenue par induction parabolique à partir d'une représentation spéciale du Levi tordue par un caractère), ainsi que les extensions de Yoneda de longueur supérieure entre séries principales modulo p sous une conjecture d'Emerton vraie pour GL2.Nous montrons de plus qu'il n'existe pas de « chaîne » de trois séries principales p-adiques ou modulo p distinctes de G. Pour cela, nous calculons partiellement le delta-foncteur H•OrdP relatif à un sous-groupe parabolique quelconque sur une série principale. En exploitant ce résultat, nous prouvons une conjecture de Breuil et Herzig sur l'unicité de certaines représentations p-adiques de G dont les constituants sont des séries principales, ainsi que son analogue modulo p.Enfin, nous énonçons une nouvelle conjecture sur les extensions entre représentations modulo p irréductibles de G obtenues par induction parabolique à partir d'une représentations supersingulière du Levi. Nous prouvons cette conjecture pour les extensions par une série principaleThis thesis is a contribution to the study of p-adic (i.e. unitary continuous on p-adic Banach spaces) and mod p (i.e. smooth over a finite field of characteristic p) representations of a split p-adic reductive group G.We determine the extensions between p-adic and mod p principal series of G. In order to do so, we compute Emerton's delta-functor H•OrdB of derived ordinary parts with respect to a Borel subgroup on a principal series using a Bruhat filtration.We also determine the extensions of a principal series by an ordinary representation (i.e. parabolically induced from a special representation of the Levi twisted by a character), as well as the Yoneda extensions of higher length between mod p principal series under a conjecture of Emerton true for GL2.Moreover, we show that there exists no “chain” of three distinct p-adic or mod p principal series of G. In order to do so, we partially compute the delta-functor H•OrdP with respect to any parabolic subgroup on a principal series. Exploiting this result, we prove a conjecture of Breuil and Herzig on the uniqueness of certain p-adic representations of G whose constituents are principal series, as well as its mod p analogue.Finally, we formulate a new conjecture on the extensions between irreducible mod p representations of G parabolically induced from a supersingular representation of the Levi. We prove this conjecture for extensions by a principal series
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Blue, Meredith Patricia. "Generic Galois extensions for groups or order p³ /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.
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Skabelund, Dane Christian. "Character Tables of Metacyclic Groups." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/3913.
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We show that any two split metacyclic groups with the same character tables are isomorphic. We then use this to show that among metacyclic groups that are either 2-groups or are of odd order divisible by at most two primes, that the dihedral and generalized quaternion groups of order 2^n, n = 3, are the only pairs that have the same character tables.
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Kennedy, Chelsea Lorraine. "Total Character Groups." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3313.
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The total character of a finite group G is the sum of the irreducible characters of G. When the total character of a finite group can be written as a monic polynomial with integer coefficients in an irreducible character of G, we say that G is a total character group. In this thesis we examine the total character of the dicyclic group of order 4n, the non-abelian groups of order p^3, and the symmetric group on n elements for all n ≥ 1. The dicyclic group of order 4n is a total character group precisely when n is congruent to 2 or 3 mod 4, and the associated polynomial is a sum of Chebyshev polynomials of the second kind. The irreducible characters paired with these polynomials are exactly the faithful characters of the dicyclic group. In contrast, the non-abelian groups of order p^3 and the symmetric group on n elements with n ≥ 4 are not total character groups. Finally, we examine the special case when G is a total character group and the polynomial is of degree 2. In this case, we say that G is a quadratic total character group. We classify groups which are both quadratic total character groups and p-groups.
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Ricciotti, Diego. "Regularity of solutions of the p-Laplace equation in the Heisenberg group." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5708/.
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Schubert, Luke. "Spectral properties of the Laplacian on p-forms on the Heisenberg group /." Title page, contents and abstract only, 1997. http://web4.library.adelaide.edu.au/theses/09PH/09phs384.pdf.
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Lechner, Sabine [Verfasser], and Annette [Akademischer Betreuer] Huber. "A comparison of locally analytic group cohomology and Lie algebra cohomology for p-adic Lie groups = Ein Vergleich lokal analytischer Gruppenkohomologie und Liealgebrenkohomologie für p-adische Liegruppen." Freiburg : Universität, 2011. http://d-nb.info/112346314X/34.
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Kahn, Eric B. "THE GENERALIZED BURNSIDE AND REPRESENTATION RINGS." UKnowledge, 2009. http://uknowledge.uky.edu/gradschool_diss/707.
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Making use of linear and homological algebra techniques we study the linearization map between the generalized Burnside and rational representation rings of a group G. For groups G and H, the generalized Burnside ring is the Grothendieck construction of the semiring of G × H-sets with a free H-action. The generalized representation ring is the Grothendieck construction of the semiring of rational G×H-modules that are free as rational H-modules. The canonical map between these two rings mapping the isomorphism class of a G-set X to the class of its permutation module is known as the linearization map. For p a prime number and H the unique group of order p, we describe the generators of the kernel of this map in the cases where G is an elementary abelian p-group or a cyclic p-group. In addition we introduce the methods needed to study the Bredon homology theory of a G-CW-complex with coefficients coming from the classical Burnside ring.
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Tallapally, Venkatesham. "Colloidal Synthesis and Photophysical Characterization of Group IV Alloy and Group IV-V Semiconductors: Ge1-xSnx and Sn-P Quantum Dots." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5568.
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Nanomaterials, typically less than 100 nm size in any direction have gained noteworthy interest from scientific community owing to their significantly different and often improved physical properties compared to their bulk counterparts. Semiconductor nanoparticles (NPs) are of great interest to study their tunable optical properties, primarily as a function of size and shape. Accordingly, there has been a lot of attention paid to synthesize discrete semiconducting nanoparticles, of where Group III-V and II-VI materials have been studied extensively. In contrast, Group IV and Group IV-V based nanocrystals as earth abundant and less-non-toxic semiconductors have not been studied thoroughly. From the class of Group IV, Ge1-xSnx alloys are prime candidates for the fabrication of Si-compatible applications in the field of electronic and photonic devices, transistors, and charge storage devices. In addition, Ge1-xSnx alloys are potentials candidates for bio-sensing applications as alternative to toxic materials. Tin phosphides, a class of Group IV-V materials with their promising applications in thermoelectric, photocatalytic, and charge storage devices. However, both aforementioned semiconductors have not been studied thoroughly for their full potential in visible (Vis) to near infrared (NIR) optoelectronic applications. In this dissertation research, we have successfully developed unique synthetic strategies to produce Ge1-xSnx alloy quantum dots (QDs) and tin phosphide (Sn3P4, SnP, and Sn4P3) nanoparticles with tunable physical properties and crystal structures for potential applications in IR technologies.
Low-cost, less-non-toxic, and abundantly-produced Ge1-xSnx alloys are an interesting class of narrow energy-gap semiconductors that received noteworthy interest in optical technologies. Admixing of α-Sn into Ge results in an indirect-to-direct bandgap crossover significantly improving light absorption and emission relative to indirect-gap Ge. However, the narrow energy-gaps reported for bulk Ge1-xSnx alloys have become a major impediment for their widespread application in optoelectronics. Herein, we report the first colloidal synthesis of Ge1-xSnx alloy quantum dots (QDs) with narrow size dispersity (3.3±0.5 – 5.9±0.8 nm), wide range of Sn compositions (0–20.6%), and composition-tunable energy-gaps and near infrared (IR) photoluminescence (PL). The structural analysis of alloy QDs indicates linear expansion of cubic Ge lattice with increasing Sn, suggesting the formation of strain-free nanoalloys. The successful incorporation of α-Sn into crystalline Ge has been confirmed by electron microscopy, which suggests the homogeneous solid solution behavior of QDs. The quantum confinement effects have resulted in energy gaps that are significantly blue-shifted from bulk Ge for Ge1-xSnx alloy QDs with composition-tunable absorption onsets (1.72–0.84 eV for x=1.5–20.6%) and PL peaks (1.62–1.31 eV for x=1.5–5.6%). Time-resolved PL (TRPL) spectroscopy revealed microsecond and nanosecond timescale decays at 15 K and 295 K, respectively owing to radiative recombination of dark and bright excitons as well as the interplay of surface traps and core electronic states. Realization of low-to-non-toxic and silicon-compatible Ge1-xSnx QDs with composition-tunable near IR PL allows the unprecedented expansion of direct-gap Group IV semiconductors to a wide range of biomedical and advanced technological studies.
Tin phosphides are a class of materials that received noteworthy interest in photocatalysis, charge storage and thermoelectric devices. Dual stable oxidation states of tin (Sn2+ and Sn4+) enable tin phosphides to exhibit different stoichiometries and crystal phases. However, the synthesis of such nanostructures with control over morphology and crystal structure has proven a challenging task. Herein, we report the first colloidal synthesis of size, shape, and phase controlled, narrowly disperse rhombohedral Sn4P3, hexagonal SnP, and amorphous tin phosphide nanoparticles (NPs) displaying tunable morphologies and size dependent physical properties. The control over NP morphology and crystal phase was achieved by tuning the nucleation/growth temperature, molar ratio of Sn/P, and incorporation of additional coordinating solvents (alkylphosphines). The absorption spectra of smaller NPs exhibit size-dependent blue shifts in energy gaps (0.88–1.38 eV) compared to the theoretical value of bulk Sn3P4 (0.83 eV), consistent with quantum confinement effects. The amorphous NPs adopt rhombohedral Sn4P3 and hexagonal SnP crystal structures at 180 and 250 °C, respectively. Structural and surface analysis indicates consistent bond energies for phosphorus across different crystal phases, whereas the rhombohedral Sn4P3 NPs demonstrate Sn oxidation states distinctive from those of the hexagonal and amorphous NPs owing to complex chemical structure. All phases exhibit N(1s) and ʋ(N-H) energies suggestive of alkylamine surface functionalization and are devoid of tetragonal Sn impurities.
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Toinet, Emmanuel. "Automorphisms of right-angled Artin groups." Thesis, Dijon, 2012. http://www.theses.fr/2012DIJOS003.
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Cette thèse a pour objet l’étude des automorphismes des groupes d’Artin à angles droits. Etant donné un graphe simple fini G, le groupe d’Artin à angles droits GG associé à G est le groupe défini par la présentation dont les générateurs sont les sommets de G, et dont les relateurs sont les commutateurs [v,w], où {v,w} est une paire de sommets adjacents. Le premier chapitre est conçu comme une introduction générale à la théorie des groupes d’Artin à angles droits et de leurs automorphismes. Dans un deuxième chapitre, on démontre que tout sous-groupe sous-normal d’indice une puissance de p d’un groupe d’Artin à angles droits est résiduellement p-séparable. Comme application de ce résultat, on montre que tout groupe d’Artin à angles droits est résiduellement séparable dans la classe des groupes nilpotents sans torsion. Une autre application de ce résultat est que le groupe des automorphismes extérieurs d’un groupe d’Artin à angles droits est virtuellement résiduellement p-fini. On montre également que le groupe de Torelli d’un groupe d’Artin à angles droits est résiduellement nilpotent sans torsion, et, par suite, résiduellement p-fini et bi-ordonnable. Dans un troisième chapitre, on établit une présentation du sous-groupe Conj(GG) deAut(GG) formé des automorphismes qui envoient chaque générateur sur un conjugué de lui-mêmeThe purpose of this thesis is to study the automorphisms of right-angled Artin groups. Given a finite simplicial graph G, the right-angled Artin group GG associated to G is the group defined by the presentation whose generators are the vertices of G, and whose relators are commuta-tors of pairs of adjacent vertices. The first chapter is intended as a general introduction to the theory of right-angled Artin groups and their automor-phisms. In a second chapter, we prove that every subnormal subgroup ofp-power index in a right-angled Artin group is conjugacy p-separable. As an application, we prove that every right-angled Artin group is conjugacy separable in the class of torsion-free nilpotent groups. As another applica-tion, we prove that the outer automorphism group of a right-angled Artin group is virtually residually p-finite. We also prove that the Torelli group ofa right-angled Artin group is residually torsion-free nilpotent, hence residu-ally p-finite and bi-orderable. In a third chapter, we give a presentation of the subgroup Conj(GG) of Aut(GG) consisting of the automorphisms thats end each generator to a conjugate of itself
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Gonda, Jessica Lynn. "Subgroups of Finite Wreath Product Groups for p=3." University of Akron / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=akron1460027790.
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Farris, Lindsey. "Normal p-Complement Theorems." Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1525865906237554.
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Ward, Robert M. "Modelling of silicon-germanium alloy heterostructures using double group formulation of k . p theory." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/9757.
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Silicon-Germanium alloy heterostructures offer the most viable opportunity to integrate electronics with optoelectronic devices for widespread commercial application. Indeed Germanium rich devices may be designed for application around 1.5 m by preying on the direct-gap energy of 890meV. Low power optical modulators operating, under the quantum confined Stark effect, at wavelength bands used in 3rd generation fibre optic communication channels are developed in this thesis from a theoretical perspective. An investigation into strained Germanium rich quantum well structures was performed, revealing information about sub-band dispersion, joint density of states and absorption coefficient using the double group formulation of k . p theory. Using zone centre eigenstates as symmetrised half integer basis functions transforming according to irreps of the double group, the spin orbit interaction is incorporated into the unperturbed Hamiltonian. Along with semi-empirical input parameters available in the literature, dispersion in bulk Silicon and Germanium reveals information about hole effective masses and indirect conduction band minima in broad agreement with experimental data. In accordance with degenerate perturbation theory; effective mass Hamiltonians, with an arbitrary quantisation axis through a canonical transformation, are constructed through a series of matrix multiplications. Retaining operator ordering allows numerical modelling of heterostructures grown on arbitrary growth planes with appropriate boundary conditions across an abrupt interface under the envelope function framework. In this thesis, the effect on the transition energy, hh1-e1, by the choice of growth plane in a quantum well heterostructure is investigated.
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Belford, Alexander. "A seismic sequence stratigraphic study of the 'Western Group Sub-basin' in permits WA-128-P and WA-211-P, Bonaparte Gulf /." Title page, contents and abstract only, 1989. http://web4.library.adelaide.edu.au/theses/09SB/09sbb428.pdf.
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Lynd, Justin. "A characterization of the 2-fusion system of L_4(q)." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1337790920.
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Wald, Christian [Verfasser], Elmar [Gutachter] Große-Klönne, Joachim [Gutachter] Mahnkopf, and Tobias [Gutachter] Schmidt. "A p-adic quantum group and the quantized p-adic upper half plane / Christian Wald ; Gutachter: Elmar Große-Klönne, Joachim Mahnkopf, Tobias Schmidt." Berlin : Humboldt-Universität zu Berlin, 2017. http://d-nb.info/118932816X/34.
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Ludsteck, Thomas. "P-adic vector bundles on curves and abelian varieties and representations of the fundamental group." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-35588.
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Mbongwa, Hlengiwe Prosperity. "Characterisation of the SULT1A1 polymorphism in a South African Tswana population group / y Hlengiwe P. Mbongwa." Thesis, North-West University, 2010. http://hdl.handle.net/10394/4225.
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This dissertation brings to the fore the “Characterization of the SULT1A1 polymorphism in a
South Africa Tswana population group.” The primary experimental group studied came from
South African homogeneous Tswana individuals who participated voluntarily in an ongoing
large-scale epidemiological Prospective Urban and Rural Epidemiological (PURE) study the
North-West University (Potchefstroom Campus) participates in, as one of the 16 low- middleand
high-income countries across the world.
The primary aspect investigated was the comprehensive profile of the single nucleotide
polymorphism (SNP) and copy number variation (CNP) of the SULT1A1 gene. Using the PCRbased
RFLP method, SULT1A1 genotypes, and allele frequency distributions in an
experimental group of 1 867 individuals were determined. According to the literature this is by
far the largest and most homogeneous group from which such information has been acquired to
date. The SULT1A1*1, SULT1A1*1/*2 and SULT1A1*2 genotypes were found to be present at
a percentage of 43.76, 47.12 and 9.11 respectively. In comparison to similar studies in other
population groups, results from this study indicate that there are ethnic differences in the
SULT1A1 genotypes incidence. Asian group differs from Caucasian and Tswana groups
because of its exceptionally high prevalence of individuals with the SULT1A1*1 genotype and a
very low incidence of the SULT1A1*2 genotype. The SULT1A1*1 genotype profiles of
Caucasian and Tswana groups were comparable, but notable differences were observed for the
SULT1A1*2 genotype.
Using a quantitative multiplex PCR method for the CNV study, the numbers of copies of the
SULT1A1 gene in the Tswana population were determined, and the results showed 1 to ~5
copies: only 0.65% of the subjects had a single copy, whereas 59.69% of the subjects had 3 or
more copies. This result shows a significant discrepancy between the Caucasian-American
samples, which showed that only 26% from that group had more than three copies. However,
there is a significant relationship with the African-American population, which presented 63%
with 3 or more copies. This finding confirms results from a much smaller African-American
study, and suggests a possible genetic link between the African Tswana and the heritage of the
African-Americans. These findings were submitted for publication to the South African Journal
of Science, as that journal specializes in publication of new knowledge that has a regional focus
on Africa. Simultaneous phenotypic consequences of the SNP and CNP of the SULT1A1 gene, as well as
the thermo-stable and thermo-labile forms of the sulfotransferases were determined. For this,
the formation of [35S]-4-nitrophenyl sulphate from 4-nitrophenol and [35S]-3’-phosphoadenosine-
5’-phosphosulfate ([35S]-PAPS) in platelet homogenates were measured, with the data
normalized to a common platelet count. This investigation required fresh blood for enzyme
activity. These samples came from 98 Caucasian subjects who voluntarily participated in this
part of the study. The experimental data presented a unique challenge to develop a statistical
model to accommodate the complexity of the distribution of the data in the phenotype and
genotype components, which could be achieved by the development of a mixed model. The
model indicated that product formation increased through increasing copy number, but did not
differ for SULT1A1*1 and SULT1A1*1/*2. However, the rate of increase in product for the
thermo-stable forms of the SULTs was greater than that of thermo-labile forms. In contrast, copy
number effect for SULT1A1*2 differed considerably from that of the other two genotypes. Since
genotype is also a significant factor, it was concluded from Tukey post-hoc tests that the
population group means for product formation differ significantly (for all levels). These results
are presently being prepared for publication in an accredited international journal.
Finally, perturbations in 23 biochemical parameters measured in the PURE study were
analyzed as a function of the SULT1A1 SNP and CNP were evaluated. No group separation in
this regard could be found. It could be shown however, that sulfonation of the iodothyronines,
which are endogenous substrates for the SULTs, was influenced by the SULT1A1 genotype.
The relative concentrations in plasma of the sulphonated iodothyronines may be expressed as
T2S > T3S >> T4S, which coincides with the substrate preference of the SULT1A1 enzymes.
This observation may, however, only be qualitatively interpreted as (1) the targeted
metabolomics mass spectrometric method used for the quantitative analysis of these
substances needs further development, and (2) the influence of deiodonation was not taken into
account in these studies. In conclusion, three perspectives are given at the end of the thesis
which might be considered for further investigations.Thesis (Ph.D. (Biochemistry))--North-West University, Potchefstroom Campus, 2010.
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Long, Jane Holsapple. "The cohomology rings of the special affine group of Fp^2 and of PSL(3,p)." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8458.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2008.Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Kreighbaum, Kevin M. "Combinatorial Problems Related to the Representation Theory of the Symmetric Group." University of Akron / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1270830566.
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Lyons, Corey Francis. "The Γ0 Graph of a p-Regular Partition." University of Akron / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1271082086.
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Gsiea, Abdusalam Mohamed Saleh. "An ab initio study of the origin of p-type doping in ZnO using group-V elements." Thesis, University of Newcastle Upon Tyne, 2011. http://hdl.handle.net/10443/1360.
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Zinc oxide is a transparent semiconductor with a direct wide band-gap 3.4 eV and large exciton binding-energy of 60 meV, that combine to make ZnO a promising material for possible applications such as optoelectronic devices, lasers and light emitting diodes. Recently, the difficulty in obtaining high quality p-type ZnO has attracted much attention. Considerable effort has been made to obtain p-type ZnO by doping with the group- V elements N, P, As, and Sb, with the anticipation of replacing oxygen atoms in the ZnO lattice. However, experimentally these dopants can produce both p-type and n-type conductivity. Here the results of first principles density functional theory calculations performed using the AIMPRO code are presented. By evaluating the relative energies of substitution on the oxygen and zinc sub-lattices, it is possible to predict the most likely forms of doping centres that might be achieved depending both upon the dopant species and whether the ZnO is grown under oxygen or zinc rich conditions. As a general trend, it is found that dopants tend to be stabilised in environments where covalent bonds with oxygen can be formed, such as substitution on the zinc sub-lattice. The doping properties of the group-V elements can be best understood by not considering the dopant atoms individually, but as a part of an atomic group such as phosphate and nitrate ions either substituting for host atoms, or lying in interstitial sites. The preferential formation of dopant-oxygen bonds leads to a revision of the zinc-vacancy based model for p-type doping (such as P-(VZn)2 complexes) to structures involving interstitial oxygen.
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Alghamdi, Ahmad M. "The Ordinary Weight conjecture and Dade's Projective Conjecture for p-blocks with an extra-special defect group." Thesis, University of Birmingham, 2004. http://etheses.bham.ac.uk//id/eprint/86/.
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Let \(p\) be a rational odd prime number, \(G\) be a finite group such that \(|G|=p^am\), with \(p \nmid m\). Let \(B\) be a \(p\)-block of \(G\) with a defect group \(E\) which is an extra-special \(p\)-group of order \(p^3\) and exponent \(p\). Consider a fixed maximal \((G, B)\)-subpair \((E, b_E)\). Let \(b\) be the Brauer correspondent of \(B\) for \(N_G(E, b_E)\). For a non-negative integer \(d\), let \(k_d(B)\) denote the number of irreducible characters \(\chi\) in \(B\) which have \(\chi(1)_p=p^{a-d}\) and let \(k_d(b)\) be the corresponding number of \(b\). Various generalizations of Alperin's Weight Conjecture and McKay's Conjecture are due to Reinhard Knorr, Geoffrey R. Robinson and Everett C. Dade. We follow Geoffrey R. Robinson's approach to consider the Ordinary Weight Conjecture, and Dade's Projective Conjecture. The general question is whether it follows from either of the latter two conjectures that \(k_d(B)=k_d(b)\) for all \(d\) for the \(p\)-block \(B\). The objective of this thesis is to show that these conjectures predict that \(k_d(B)=k_d(b)\), for all non-negative integers \(d\). It is well known that \(N_G(E, b_E)/EC_G(E)\) is a \(p^'\)-subgroup of the automorphism group of \(E\). Hence, we have considered some special cases of the above question.The unique largest normal \(p\)-subgroup of \(G\), \(O_p(G)\) is the central focus of our attention. We consider the case that \(O_p(G)\) is a central \(p\)-subgroup of \(G\), as well as the case that \(O_p(G)\) is not central. In both cases, the common factor is that \(O_p(G)\) is strictly contained in the defect group of \(B\).
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Bailly, Pascal. "Etude de la biosynthese des antigenes de groupes sanguins p : :(1) et p**(k)." Paris 7, 1988. http://www.theses.fr/1988PA077007.
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CHINELLO, GIANMARCO. "Représentations l-modulaires des groupes p-adiques. Décomposition en blocs de la catégorie des représentations lisses de GL(m,D), groupe métaplectique et représentation de Weil." Doctoral thesis, Université de Versailles St-Quentin-en-Yvelines, 2015. http://hdl.handle.net/10281/123569.
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This thesis focuses on two problems on l-modular representation theory of p-adic groups. Let F be a non-archimedean local field of residue characteristic p different from l. In the first part, we study block decomposition of the category of smooth modular representations of GL(n; F) and its inner forms.We want to reduce the description of a positive-level
block to the description of a 0-level block (of a similar group) seeking equivalences of categories. Using the type theory of Bushnell-Kutzko in the modular case and a theorem of category theory, we reduce the problem to find an isomorphism between two intertwining algebras. The proof of the existence of such an isomorphism is not complete because it
relies on a conjecture that we state and we prove for several cases. In the second part we generalize the construction of metaplectic group and Weil representation in the case of representations over un integral domain. We define a central extension of the symplectic group over F by the multiplicative group of an integral domain. We prove that it satisfies
the same properties as in the complex case.Cette thèse traite deux problèmes concernant la théorie des représentations l-modulaires d’un groupe p-adique. Soit F un corps local non archimédien de caractéristique résiduelle p différente de l. Dans la première partie, on étudie la décomposition en blocs de la catégorie des représentations lisses `-modulaires de GL(n; F) et de ses formes intérieures. On veut ramener la description d’un bloc de niveau positif à celle d’un bloc de niveau 0 (d’un autre groupe du même type) en cherchant des équivalences de catégories. En utilisant la théorie des types de Bushnell-Kutzko dans le cas modulaire et un théorème de la théorie des catégories, on se ramene à trouver un isomorphisme entre deux algèbres d’entrelacement. La preuve de l’existence d’un tel isomorphisme n’est pas complète car elle repose sur une conjecture qu’on énonce et qui est prouvée pour plusieurs cas. Dans une deuxième partie on généralise la construction du groupe métaplectique et de la représentation de Weil dans le cas des représentations sur un anneau intègre. On construit une extension centrale du groupe symplectique sur F par le groupe multiplicatif d’un anneau intègre et on prouve qu’il satisfait les mêmes propriétés que dans le cas des représentations complexes.
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Carvalho, Rafaela Soares de [UNESP]. "Singularidades do tipo D(q,p)." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/137928.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Neste trabalho estudamos germes de funções sob a ação do grupo R_I dos germes de difeomorfismos em C^n que preservam um ideal I, descrevendo os conceitos de codimensão e determinação finita associados. Isso nos fornece ferramentas para caracterizar um tipo especial de germes com singularidades não isoladas, as chamadas singularidades do tipo D(q,p). Conseguimos ainda relacionar o conceito de R_I-estabilidade com estes germes, para o caso em que I é um ideal radical que define uma intersecção completa quase homogênea com singularidade isolada. Além disso, apresentamos um sistema de coordenadas através do qual obtemos uma fórmula explícita para alguns dos números de Lê destes germes.
In this work we study germs of functions under the action of the R_I group of diffeomorphisms of germs in C^n which preserving an ideal I, describing the concepts of codimension and finite determination associated. This provides the tools to characterize a particular type of germ with non isolated singularities, the so called D(q,p) singularities. We can still relate the concept of R_I-stability with these germs, in the case where I is a radical ideal that defines complete intersection with isolated singularity. Moreover, we present a coordinate system by which we obtain an explicit formula for some Lê numbers of these germs.
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Maakestad, Helge. "Principal Parts on P^1 and Chow-groups of the classical discriminants." Doctoral thesis, KTH, Mathematics, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3022.
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