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Dissertations / Theses on the topic 'Solvable groups'
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1
Bissler, Mark W. "Character degree graphs of solvable groups." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1497368851849153.
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Wetherell, Chris. "Subnormal structure of finite soluble groups." View thesis entry in Australian Digital Theses Program, 2001. http://thesis.anu.edu.au/public/adt-ANU20020607.121248/index.html.
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Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.
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The conjugacy length function of a group Γ determines, for a given a pair of conjugate elements u,v ∈ Γ, an upper bound for the shortest γ in Γ such that uγ = γv, relative to the lengths of u and v. This thesis focuses on estimating the conjugacy length function in certain finitely generated groups. We first look at a collection of solvable groups. We see how the lamplighter groups have a linear conjugacy length function; we find a cubic upper bound for free solvable groups; for solvable Baumslag--Solitar groups it is linear, while for a larger family of abelian-by-cyclic groups we get either a linear or exponential upper bound; also we show that for certain polycyclic metabelian groups it is at most exponential. We also investigate how taking a wreath product effects conjugacy length, as well as other group extensions. The Magnus embedding is an important tool in the study of free solvable groups. It embeds a free solvable group into a wreath product of a free abelian group and a free solvable group of shorter derived length. Within this thesis we show that the Magnus embedding is a quasi-isometric embedding. This result is not only used for obtaining an upper bound on the conjugacy length function of free solvable groups, but also for giving a lower bound for their Lp compression exponents. Conjugacy length is also studied between certain types of elements in lattices of higher-rank semisimple real Lie groups. In particular we obtain linear upper bounds for the length of a conjugator from the ambient Lie group within certain families of real hyperbolic elements and unipotent elements. For the former we use the geometry of the associated symmetric space, while for the latter algebraic techniques are employed.
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Bleak, Collin. "Solvability in groups of piecewise-linear homeomorphisms of the unit interval." Diss., Online access via UMI:, 2005.
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Vershik, A. M., and Andreas Cap@esi ac at. "Geometry and Dynamics on the Free Solvable Groups." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi899.ps.
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Roth, Calvin L. (Calvin Lee). "Example of solvable quantum groups and their representations." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28104.
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Yang, Yong. "Orbits of the actions of finite solvable groups." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0024783.
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Dugan, Carrie T. "Solvable Groups Whose Character Degree Graphs Have Diameter Three." Kent State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=kent1185299573.
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Vassileva, Svetla. "The word and conjugacy problems in classes of solvable groups." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66827.
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This thesis is a survey of certain algorithmic problems in group theory and their computational complexities. In particular, it consists of a detailed review of the decidability and complexity of the word and conjugacy problems in several classes of solvable groups, followed by two original results. The first result states that the Conjugacy Problem in wreath products which satisfy certain elementary conditions is decidable in polynomial time. It is largely based on work by Jane Matthews, published in 1969. The second result, based on ideas of Remeslennikov and Sokolov (1970), and Myasnikov, Roman'kov, Ushakov and Vershik (2008) gives a uniform polynomial time algorithm to decide the Conjugacy Problem in free solvable groups.Cette thèse est une synthèse de certains problèmes algorithmiques dans la thèoriedes groupes et leur complexité computationnelle. Plus particulièrement, elle présenteune revue détaillée de la décidabilité et de la complexité des problèmes du mot et dela conjugaison dans plusieurs classes de groupes solubles, suivie de deux nouveauxrésultats. Le premier résultat énonce que le problème de la conjugaison dans lesproduits couronne qui satisfont certaines conditions élémentaires est décidable entemps polynomial. Elle part d'une publication de Jane Matthews (1969). Le deuxièmerésultat, basé sur des idées de Remeslennikov et Sokolov (1970) et de Myasnikov, Roman'kov,Ushakov et Vershik (2008), présente un algorithme en temps polynomial uniformepour décider le problème de conjugaison dans les groupes solubles libres.
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Sass, Catherine Bray. "Prime Character Degree Graphs of Solvable Groups having Diameter Three." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1398110266.
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Psaras, Emanuel S. "A Study of Fixed-Point-Free Automorphisms and Solvable Groups." Youngstown State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1588762170044899.
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Decker, Erin. "On the construction of groups with prescribed properties." Diss., Online access via UMI:, 2008.
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Thomas, Teri M. "A generalization of Sylow's theorem /." Connect to resource online, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1256911896.
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Torres, Bisquertt María de la Luz. "Symmetric generation of finite groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2625.
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Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.
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Mebane, Palmer. "Uniquely Solvable Puzzles and Fast Matrix Multiplication." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/37.
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In 2003 Cohn and Umans introduced a new group-theoretic framework for doing fast matrix multiplications, with several conjectures that would imply the matrix multiplication exponent $\omega$ is 2. Their methods have been used to match one of the fastest known algorithms by Coppersmith and Winograd, which runs in $O(n^{2.376})$ time and implies that $\omega \leq 2.376$. This thesis discusses the framework that Cohn and Umans came up with and presents some new results in constructing combinatorial objects called uniquely solvable puzzles that were introduced in a 2005 follow-up paper, and which play a crucial role in one of the $\omega = 2$ conjectures.
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Wood, Lisa M. "ON THE SOLVABLE LENGTH OF ASSOCIATIVE ALGEBRAS, MATRIX GROUPS, AND LIE ALGEBRAS." NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-10272004-164622/.
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Let A be an algebraic system with product a*b between elements a and b in A. It is of interest to compare the solvable length t with other invariants, for instance size, order, or dimension of A. Thus we ask, for a given t what is the smallest n such that there is an A of length t and invariant n. It is this problem that we consider for associative algebras, matrix groups, and Lie algebras. We consider A in each case to be subsets of (strictly) upper triangular n by n matrices. Then the invariant is n. We do these for the associative (Lie) algebras of all strictly upper triangular n by n matrices and for the full n by n upper triangular unipotent groups. The answer for n is the same in all cases. Then we restrict the problem to a fixed number of generators. In particular, using only 3 generators and we get the same results for matrix groups and Lie algebras as for the earlier problem. For associative algebras with 1 generator we also get the same result as the general associative algebra case. Finally we consider Lie algebras with 2 generators and here n is larger than in the general case. We also consider the problem of finding the dimension in the associative algebra, the general, and 3 generator Lie algebra cases.
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Mohammed, Zakiyah. "Carter Subgroups and Carter's Theorem." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1310158687.
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ELSHARIF, RAMADAN. "The Average of Some Irreducible Character Degrees." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1616410634054592.
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Santos, Edson Carlos Licurgo. "Estruturas complexas comauto-espaços nilpotentes e soluveis." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305823.
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Orientador: Luiz Antonio Barrera San MartinTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-10T11:48:47Z (GMT). No. of bitstreams: 1 Santos_EdsonCarlosLicurgo_D.pdf: 405695 bytes, checksum: 334d5172d85f7bc35539dbd900fbef67 (MD5) Previous issue date: 2007
Resumo: Seja (g; [·,·]) uma álgebra de Lie com uma estrutura complexa integrável J. Os ± i-auto-espaços de J são subálgebras complexas de gC isomorfas a álgebra (g; [*]J ) com colchete [X * Y ]J = ½ ([X, Y ] - [JX, JY ]). Consideramos, no capítulo 2, o caso onde estas subálgebras são nilpotentes e mostramos que a álgebra de Lie original (g, [·,·]) é solúvel. Consideramos também o caso 6-dimensional e determinamos explicitamente a única álgebra de Lie possível (g; [*]J ). Finalizamos esse capítulo pruduzindo vários exemplos ilustrando diferentes situações, em particular mostramos que para cada s existe g com estrutura complexa J tal que (g; [*]J ) é s-passos nilpotente. Exemplos similares para estruturas hipercomplexas são também construidos. No capítulo 3 consideramos o caso onde os ±i-auto-espaços de J são subálgebras complexas solúveis e a álgebra complexa é uma álgebra de Lie semi-simples. Mostramos que, se a álgebra real é compacta, uma tal estrutura complexa depende unicamente de um subespaço da subálgebra de Cartan. Finalizamos esse capítulo considerando o caso em que as subálgebras solúveis complexas estão contidas em subálgebras de Borel de uma órbita aberta da ação dos automorfismos internos da álgebra real. Mostramos que, assim como no caso compacto, as estruturas complexas são determinandas, de modo único, por subespaços da subálgebra de Cartan. Ao final da tese apresentamos um procedimento, elaborado em MAPLE, que possibilita testar a identidade de Jacobi quando os colchetes de Lie são dados pelas constantes de estrutura
Abstract: Let (g; [·,·]) be a Lie algebra with an integrable complex structure J. The ±i eigenspaces of J are complex subalgebras of gC isomorphic to the algebra (g; [*]J )with bracket [X * Y ]J = ½ ([X, Y ] - [JX, JY ]). We consider, in chapter three, thecase where these subalgebras are nilpotent and prove that the original Lie algebra(g, [·,·]) must be solvable. We consider also the 6-dimensional case and determineexplicitly the possible nilpotent Lie algebras (g; [*]J ). We finish this chapter byproducing several examples illustrating different situations, in particular we showthat for each given s there exists g with complex structure J such that (g; [*]J ) iss-step nilpotent. Similar examples of hypercomplex structures are also built.In Chapter 3 we consider the case where the ± i eigenspaces of J are solvablecomplex subalgebras and gC is a semisimple Lie algebra. We prove that, if g is compact, such a complex structure comes from a subspace of the Cartan subalgebra.We finish this chapter by considering the case where the solvable complex subalgebras are contained in Borel subalgebras of an open orbit of the action of inner automorphisms of the real algebra.At the end of the thesis we present an algorithm, made in MAPLE, that allowus to verify the Jacobi identity when the Lie brackets are defined by the structureconstants
Doutorado
Mestre em Matemática
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Qi, Dongwen. "On irreducible, infinite, non-affine coxeter groups." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1185463175.
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Zergane, Amel. "Séparation des représentations des groupes de Lie par des ensembles moments." Thesis, Dijon, 2011. http://www.theses.fr/2011DIJOS086/document.
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Si (π, H) est une représentation unitaire irréductible d'un groupe de Lie G, on sait lui associer son application moment Ψπ. La fermeture de l'image de Ψπ s'appelle l'ensemble moment de π. Généralement, cet ensemble est Conv(Oπ), si Oπ est l'orbite coadjointe associée à π. Mais il ne caractérise pas π : deux orbites distinctes peuvent avoir la même enveloppe convexe fermée. On peut contourner cette non séparation en considérant un surgroupe G+ de G et une application non linéaire ø de g* dans (g+)* telle que, pour les orbites générique, ø(O) est une orbite et Conv (ø(O)) caractérise O. Dans cette thèse, on montre que l'on peut choisir le couple (G+, ø), avec ø de degré ≤ 2 pour tous les groupes nilpotents de dimension ≤ 6, à une exception près, tous les groupes résolubles de dimension ≤ 4, et pour un exemple de groupe de déplacements. Ensuite, on étudie le cas des groupes G = SL(n, R). Pour ces groupes, il existe un tel couple avec ø de degré n, mais il n'en existe pas avec ø de degré 2 si n>2, il n'en existe pas avec ø de degré 3 si n=4. Enfin, on montre que l'application moment Ψπ est celle d'une action fortement hamiltonienne de G sur la variété de Fréchet symplectique PH∞. On construit un foncteur qui associe à tout G un surgroupe de Lie Fréchet G̃, de dimension infinie et, à tout π de G, une action π̃ fortement hamiltonienne, dont l'ensemble moment caractérise πTo a unitary irreducible representation (π,H) of a Lie group G, is associated a moment map Ψπ. The closure of the range of Ψπ is the moment set of π. Generally, this set is Conv(Oπ), if Oπ is the corresponding coadjoint orbit. Unfortunately, it does not characterize π : 2 distincts orbits can have the same closed convex hull. We can overpass this di culty, by considering an overgroup G+ for G and a non linear map ø from g* into (g+)* such that, for generic orbits, ø(O) is an orbit and Conv( ø(O)) characterizes O. In the present thesis, we show that we can choose the pair (G+,ø), with deg ø ≤2 for all the nilpotent groups with dimension ≤6, except one, for all solvable groups with diemnsion ≤4, and for an example of motion group. Then we study the G=SL(n,R) case. For these groups, there exists ø with deg ø =n, if n>2, there is no such ø with deg ø=2, if n=4, there is no such ø with deg ø=3. Finally, we show that the moment map Ψπ is coming from a stronly Hamiltonian G-action on the Frécht symplectic manifold PH∞. We build a functor, which associates to each G an infi nite diemnsional Fréchet-Lie overgroup G̃,and, to each π a strongly Hamiltonian action, whose moment set characterizes π
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Zelaya, Carlos A. "6,6’-Dimethoxygossypol: Molecular Structure, Crystal Polymorphism, and Solvate Formation." ScholarWorks@UNO, 2011. http://scholarworks.uno.edu/td/136.
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6,6’-Dimethoxygossypol (DMG) is a natural product of the cotton variety Gossypium barbadense and a derivative of gossypol. Gossypol has been shown to form an abundant number of clathrates with a large variety of compounds. One of the primary reasons why gossypol can form clathrates has been because of its ability to from extensive hydrogen bonding networks due to its hydroxyl and aldehyde functional groups. Prior to this work, the only known solvate that DMG formed was with acetic acid. DMG has methoxy groups substituted at two hydroxyl positions, and consequently there is a decrease in its ability to form hydrogen bonds. Crystallization experiments were set up to see whether, like gossypol, DMG could form clathrates. The following results presented prove that DMG is capable of forming clathrates (S1 and S2) and two new polymorphs (P1 and P2) of DMG have been reported.
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Sircana, Carlo [Verfasser], and Claus [Akademischer Betreuer] Fieker. "On the construction of number fields with solvable Galois group / Carlo Sircana ; Betreuer: Claus Fieker." Kaiserslautern : Technische Universität Kaiserslautern, 2021. http://d-nb.info/1236571916/34.
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Aziziheris, Kamal. "Determining Group Structure From the Sets of Character Degrees." Kent State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=kent1292619355.
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Gutierrez, Renan Campos. "O teorema da alternativa de Tits." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-05092012-113104/.
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Este projeto de mestrado tem por objetivo dar uma prova elementar do seguinte teorema de Tits, conhecido como Teorema da Alternativa de Tits: Seja G um grupo linear finitamente gerado sobre um corpo. Então G é solúvel por finito ou G contém um grupo livre não cíclico. Este teorema, que foi provado por J. Tits em 1972 [4], foi considerado pelo matemático J.P. Serre como um dos mais importantes resultados de álgebra do século XX. Quando dizemos uma prova elementar, não queremos absolutamente te dizer uma prova simples. Seguiremos a prova simplificada de John D. DixonThis masters project aims to give an elementary proof of the following theorem of Tits, known as the Alternative Tits Theorem: Let G be a finitely generated linear group over a field. Then either G is solvable by finite or G contains a noncyclic free subgroup. This theorem was proved by J. Tits in 1972 [4], was considered by the mathematician J.P. Serre, as one of the most important algebra results of the XX century. When we say an elementary proof, we absolutely not mean a simple proof. We will follow the simplified proof of John D. Dixon
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Turkan, Erkan Murat. "On The Index Of Fixed Point Subgroup." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613522/index.pdf.
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Let G be a finite group and A be a subgroup of Aut(G). In this work, we studied the influence of the index of fixed point subgroup of A in G on the structure of G.
When A is cyclic, we proved the following:
(1) [G,A] is solvable if this index is squarefree and the orders of G and A are coprime.
(2) G is solvable if the index of the centralizer of each x in H-G is squarefree where H denotes the semidirect product of G by A.
Moreover, for an arbitrary subgroup A of Aut(G) whose order is coprime to the order of G, we showed that when G is solvable, then the Fitting length f([G,A]) of [G,A] is bounded above by
the number of primes (counted with multiplicities) dividing the index of fixed point subgroup of A in G and this bound is best possible.
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Kouki, Sami. "Étude des restrictions des séries discrètes de certains groupes résolubles et algébriques." Thesis, Poitiers, 2014. http://www.theses.fr/2014POIT2257/document.
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Soit G un groupe de Lie résoluble connexe et H un de ses sous-groupes fermés connexes d'algèbres de Lie g et h respectivement. On note g* (resp. h*) le dual linéaire de g (resp. h) ). Le sujet de ma thèse consiste à étudier la restriction d'une série discrète π de G, associée à une orbite coadjointe Ω C g*, à H. Si la restriction de π à H se décompose en somme directe de représentations de H avec multiplicités finies, on dit que π est H-admissible. Notons Pg,n : Ω → h* l'application restriction. Il s'agit de démontrer la conjecture suivante due à Michel Duflo : 1. La représentation π est H-admissible si et seulement si l'application moment Pg,n est propre sur l'image. 2. Si π est H-admissible, et si T est une série discrète de H alors sa multiplicité dans la restriction de π à H doit pouvoir se calculer en « quantifiant » l'espace réduit correspondant (qui est compact dans ce cas). Dans cette thèse, nous apportons une réponse positive à cette conjecture dans deux situations, à savoir :(i) Le groupe G est résoluble exponentiel. (ii) Le groupe G est le produit semi direct d'un tore compact par le groupe de Heisenberg et H est un sous-groupe algébrique connexeLet G be a connected solvable Lie group and H a closed connected subgroup with Lie algebra g and h respectively. We denote g* (resp. h*) the dual of g (resp. h). The aim of my thesis is to study the restriction of a discrete series π of G, associated with a coadjoint orbit Ω C g* to H. If the restriction of π to H can be decomposed in to a direct sum of representations of H with finite multiplicities, we say that π is H-admissible. Let Pg,n : Ω → h* denote the restriction map. My objective is to show the following conjecture due to Michel Duflo : 1. The representation π i s H-admissible if and only if the moment application Pg,n is proper on the image. 2. If π is H-admissible, and if T is a discrete series of H then it s multiplicity in the restriction of π to H must be calculated by « quantifying » the corresponding reduced space (that is compact in this case). In this thesis, we provide a positive response to this conjecture in two situations, namely when: (i) G is exponential solvable Lie group. (ii) G is the semi direct product of a compact torus and the Heisenberg group and H is a connected algebraic subgroup
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Lyons, Corey Francis. "INDUCED CHARACTERS WITH EQUAL DEGREE CONSTITUENTS." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1461594819.
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Thiery, Thimothée. "Analytical methods and field theory for disordered systems." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE017/document.
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Cette thèse présente plusieurs aspects de la physique des systèmes élastiques désordonnés et des méthodes analytiques utilisées pour les étudier. On s’intéressera d’une part aux propriétés universelles des processus d’avalanches statiques et dynamiques (à la transition de dépiégeage) d’interfaces élastiques de dimension arbitraire en milieu aléatoire à température nulle. Pour étudier ces questions nous utiliserons le groupe de renormalisation fonctionnel. Après une revue de ces aspects,nous présenterons plus particulièrement les résultats obtenus pendant la thèse sur (i) la structure spatiale des avalanches et (ii) les corrélations entre avalanches.On s’intéressera d’autre part aux propriétés statiques à température finie de polymères dirigés en dimension 1+1, et en particulier aux observables liées à la classe d’universalité KPZ. Dans ce contexte l’étude de modèles exactement solubles a récemment permis de grands progrès. Après une revue de ces aspects, nous nous intéresserons plus particulièrement aux modèles exactement solubles de polymère dirigé sur le réseau carré, et présenterons les résultats obtenus pendantla thèse dans cette voie: (i) classification des modèles à température finie sur le réseau carré exactement solubles par ansatz de Bethe; (ii) universalité KPZ pour les modèles Log-Gamma et Inverse-Beta; (iii) universalité et nonuniversalitéKPZ pour le modèle Beta; (iv) mesures stationnaires du modèle Inverse-Beta et des modèles à température nulle associésThis thesis presents several aspects of the physics of disordered elastic systems and of the analytical methods used for their study.On one hand we will be interested in universal properties of avalanche processes in the statics and dynamics (at the depinning transition) of elastic interfaces of arbitrary dimension in disordered media at zero temperature. To study these questions we will use the functional renormalization group. After a review of these aspects we will more particularly present the results obtained during the thesis on (i) the spatial structure of avalanches and (ii) the correlations between avalanches.On the other hand we will be interested in static properties of directed polymers in 1+1 dimension, and in particular in observables related to the KPZ universality class. In this context the study of exactly solvable models has recently led to important progress. After a review of these aspects we will be more particularly interested in exactly solvable models of directed polymer on the square lattice and present the results obtained during the thesis in this direction: (i) classification ofBethe ansatz exactly solvable models of directed polymer at finite temperature on the square lattice; (ii) KPZ universality for the Log-Gamma and Inverse-Beta models; (iii) KPZ universality and non-universality for the Beta model; (iv) stationary measures of the Inverse- Beta model and of related zero temperature models
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Benjamin, Diane Mullan. "Character degrees and structure of solvable and p-solvable groups." 1997. http://catalog.hathitrust.org/api/volumes/oclc/37959599.html.
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Thesis (Ph. D.)--University of Wisconsin--Madison, 1997.Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 54-55).
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Lewis, Mark Lanning. "A new character correspondence for solvable groups." 1995. http://catalog.hathitrust.org/api/volumes/oclc/33663656.html.
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Thesis (Ph. D.)--University of Wisconsin--Madison, 1995.Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 131).
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Hamblin, James. "On solvable groups satisfying the two-prime hypothesis." 2002. http://www.library.wisc.edu/databases/connect/dissertations.html.
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Newton, Benjamin Willard. "Complex p-solvable linear groups of finite order." 2006. http://catalog.hathitrust.org/api/volumes/oclc/83777251.html.
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Ali, Asif. "Supersoluble groups of Wielandt length two." Phd thesis, 1997. http://hdl.handle.net/1885/145328.
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Short, M. W. "The primitive soluble permutation groups of degree less than 256." Phd thesis, 1990. http://hdl.handle.net/1885/139503.
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Wängefors, Magnus. "Estimates for Riesz operators on some solvable lie groups." 2000. http://catalog.hathitrust.org/api/volumes/oclc/48798876.html.
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Marshall, Mary K. "Derived lengths of solvable groups with abelian Sylow subgroups." 1993. http://catalog.hathitrust.org/api/volumes/oclc/30117461.html.
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Thesis (Ph. D.)--University of Wisconsin--Madison, 1993.Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 44).
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Riedl, Jeffrey Mark. "Fitting heights of solvable groups with few irreducible character degrees." 1998. http://catalog.hathitrust.org/api/volumes/oclc/40810140.html.
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Thesis (Ph. D.)--University of Wisconsin--Madison, 1998.Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 61).
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Smith, Michael J. "Computing automorphisms of finite soluble groups." Phd thesis, 1994. http://hdl.handle.net/1885/133102.
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There is a large collection of effective algorithms for computing information
about finite soluble groups. The success in computation with these groups is
primarily due to a computationally convenient representation of them by means
of (special forms of) power conjugate presentations. A notable omission from this
collection of algorithms is an effective algorithm for computing the automorphism
group of a finite soluble group. An algorithm designed for finite groups in general
provides only a partial answer to this deficiency.
In this thesis an effective algorithm for computing the automorphism group
of a finite soluble group is described. An implementation of this algorithm has
proved to be a substantial improvement over existing techniques available for finite
soluble groups.
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Chen, Ingrid. "Partial complements in finite soluble groups." Phd thesis, 2012. http://hdl.handle.net/1885/149677.
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Let G be a finite group with normal subgroup N. Let K be a subgroup of G. We say that K is a partial complement of N in G if N and K intersect trivially. There are two main results in this work. The first main result arises from analysing when each partial complement of N in G is contained in a complement of N in G when G is a finite soluble group, N is the product of minimal normal subgroups, N is complemented and all the complements of N in G are conjugate. We show that each partial complement of N in G is contained in a complement of N in G if and only if N is projective. The next natural question is: if N is non-projective, which partial complements are contained in a complement of N in G? We say that a cyclic p-partial complement is a partial complement that is cyclic and its order is a power of p. We establish exactly which cyclic p-partial complements are contained in a conjugate of H.
So the next question is: if the partial complement is a non-cyclic p-partial complement, how do we know that is contained in a conjugate of H? This is a difficult question and because of restriction on representation theory, we have needed to restrict H to be in the class of groups that are nilpotent p'-groups by p-groups. To answer this question, we use the first cohomology group. The first cohomology group is the number of conjugacy classes of complements to N in G. That is, if we have a partial complement K such that the first cohomology group vanishes then we know there is only one conjugacy class of complements of N in NK and therefore K is in a conjugate of H. The second main result finds exactly when the first cohomology group vanishes. This is a sufficient condition for a partial complement to be contained in a complement of N in G. -- provided by Candidate.
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Niemeyer, Alice C. "Computing presentations for finite soluble groups." Phd thesis, 1993. http://hdl.handle.net/1885/133191.
Full textAbstract:
The work in this thesis was carried out in the area of computational group
theory. The latter is concerned with designing algorithm s and developing their
practical implementations for investigating problem s regarding groups. An important class of groups are finite soluble groups. These can be described in a
computationally convenient way by power conjugate presentations. In practice,
however, they are usually supplied differently. The aim of this thesis is to propose
algorithm s for computing power conjugate presentations for finite soluble groups.
This is achieved in two different ways.
One of the ways in which a finite soluble group is often supplied is as a quotient
of a finitely presented group. T he first p art of the thesis is concerned with designing
an algorithm to compute a power conjugate presentation for a finite soluble group
given in this way. T he theoretical background for the algorithm is provided and
its practicality is investigated on an implementation.
T he second p a rt of the thesis describes the theoretical aspects of an algorithm
to compute all pow er conjugate presentations for a certain class of finite soluble
groups of a given order.
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Jarso, Tamiru. "Automorphisms fixing subnormal subgroups of certain infinite soluble groups." Phd thesis, 2003. http://hdl.handle.net/1885/148800.
Full text
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Lin, Cheng-Chieh, and 林正傑. "Irreducible Characters and Taketa's Inequality for Finite Solvable PC-Groups of First Type." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/67973923203328288235.
Full textAbstract:
碩士國立高雄師範大學
數學系
93
A finite group is said to be power-commutative ($PC$) if the commutativity of nontrivial powers of two elements implies the commutativity of the two elements. We study irreducible characters of finite solvable $PC$-groups of first type and related problems to the Taketa's inequality in this article.
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Tolcachier, Alejandro. "Grupos de Bieberbach y holonomía de solvariedades planas." Bachelor's thesis, 2018. http://hdl.handle.net/11086/11323.
Full textAbstract:
Tesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2018.Una solvariedad es una variedad compacta de la forma L/G donde G es un grupo de Lie soluble simplemente conexo y L es un retículo de G. En este trabajo estudiamos solvariedades equipadas con una métrica riemanniana plana, a partir de la caracterización dada por Milnor de los grupos de Lie que admiten una métrica riemanniana invariante a izquierda plana. Las solvariedades planas son ejemplos de variedades compactas planas, por lo cual podemos aplicar los teoremas clásicos de Bieberbach para describir el grupo fundamental L de la variedad L/G. En particular, todo grupo de Bieberbach posee un subgrupo abeliano maximal de índice finito. Más aún, el cociente del grupo L por este subgrupo es finito y se identifica con la holonomía riemanniana de la variedad compacta plana. Probamos primero que el grupo de holonomía riemanniana de cualquier solvariedad plana es abeliano y que todo grupo abeliano finito se puede obtener así. Luego, nos restringimos al caso de grupos de Lie casi abelianos, para los cuales hay un criterio para determinar la existencia de retículos, el cual utilizamos para clasificar las solvariedades planas en dimensión 3, 4 y 5. Para dimensiones mayores, probamos que para todo n>2 la dimensión mínima de una variedad compacta plana con grupo de holonomía Z_n coincide con la dimensión mínima de una solvariedad plana con grupo de holonomía Z_n.
A solvmanifold is a compact manifold L/G where G is a simply connected solvable Lie group and L is a lattice of G. In this article we study solvmanifolds equipped with a flat Riemannian metric, according to Milnor's characterization of Lie groups that admit a flat left invariant metric. Flat solvmanifolds are examples of compact flat manifolds, so we can apply the classic theory of Bieberbach groups to describe the fundamental group L of the manifold L/G. In particular, every Bieberbach group has a maximal normal abelian subgroup which has finite index. Fruthermore, the quotient of the group L by this subgroup is finite and can be with the riemannian holonomy group of the compact flat manifold. First, we prove that the holonomy group of every flat solvmanifold is abelian and, conversely, that every finite abelian group can be obtained as a holonomy group of a flat solvmanifold. Then, we focus on almost abelian Lie groups, for which there is a well known criterion to determine the existence of lattices that we use to classify flat solvmanifolds of dimension 3, 4 and 5. Concerning arbitrary dimensions, we prove that for every n>2 the minimum dimension of a compact flat manifold with holonomy group Z_n is equal to the minimum dimension of a flat solvmanifold with holonomy group Z_n.
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Gallo, Andrea Lilén. "Análisis armónico en nilvariedades." Doctoral thesis, 2020. http://hdl.handle.net/11086/15949.
Full textAbstract:
Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2020.Esta tesis se encuadra en el estudio del análisis armónico en pares de Gelfand de la forma (K,N), donde N es un grupo de Lie nilpotente y K es un subgrupo de automorfismos de N. En una primera parte trabajamos con una familia de pares de Gelfand (K,N) definida previamente por Jorge Lauret. Descomponemos la acción del producto semidirecto de K y N, sobre el espacio de funciones definidas sobre N de cuadrado integrable. Para estas familias, encontramos además la medida de Plancherel y la proyección sobre cada componente mediante las funciones esféricas asociadas al par. En el caso del grupo de Heisenberg se obtienen estos resultados para los pares de Gelfand asociados a cualquier K subgrupo de automorfismos del grupo de Heisenberg. Finalmente, nos avocamos al estudio de pares de Gelfand generalizados, es decir, a pares de Gelfand donde el subgrupo K no es necesariamente compacto. Un resultado clásico garantiza que si (K,N) es un par de Gelfand donde N es un grupo de Lie nilpotente y K subgrupo compacto de automorfismos de N, entonces N es a lo sumo 2-pasos nilpotente. En esta tesis, damos un ejemplo concreto de un par de Gelfand generalizado (K,N) donde N es un grupo de Lie 3-pasos nilpotente.
This thesis is part of the study of harmonic analysis in Gelfand pairs (K,N), where N is a nilpotent Lie group and K a subgroup of automorphisms of N. In the first part, we work with a family of Gelfand pairs (K,N) defined by Jorge Lauret. We decompose the action of the semidirect product of K and N in the space of square integrable functions defined on N. We also find the Plancherel measure and the projection over each component by using spherical functions associated to the pair. In the Heisenberg case we obtain similar results with every Gelfand pair associated with each automorphism subgroup of the Heisenberg group. Finally, we deal with the study of generalized Gelfand pairs, i.e when K is non-compact. A classic result assures that, if (K,N) is a Gelfand pair with N nilpotent and K compact then N is necessarily 2-step nilpotent. In this thesis, we give an explicit example of a generalized Gelfand pair (K,N) where N is a 3-step nilpotent Lie group.
Fil: Gallo, Andrea Lilén. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
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Origlia, Marcos Miguel. "Estructuras localmente conformes Kähler y localmente conformes simplécticas en solvariedades compacta." Doctoral thesis, 2017. http://hdl.handle.net/11086/5837.
Full textAbstract:
Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2017.En esta tesis estudiamos las estructuras localmente conformes Kähler (LCK) y localmente conformes simplécticas (LCS) invariantes a izquierda en grupos de Lie, o equivalentemente tales estructuras en álgebras de Lie. Luego se buscan retículos (subgrupos discretos co-compactos) en dichos grupos. De esta manera obtenemos estructuras LCK o LCS en las solvariedades compactas (cociente de un grupo de Lie por un retículo). Específicamente estudiamos las estructuras LCK en solvariedades con estructuras complejas abelianas. Luego describimos explícitamente la estructura de las álgebras de Lie que admiten estructuras de Vaisman. También determinamos los grupos de Lie casi abelianos que admiten estructuras LCK o LCS y además analizamos la existencia de retículos en ellos. Finalmente desarrollamos un método para construir de manera sistemática ejemplos de álgebras de Lie equipadas con estructuras LCK o LCS a partir de un álgebra de Lie que ya admite tales estructuras y una representación compatible.
In this thesis we study left invariant locally conformal Kähler (LCK) structures and locally conformal symplectic structures (LCS) on Lie groups, or equivalently such structures on Lie algebras. Then we analize the existence of lattices (co-compact discrete subgroups) on these Lie groups. Therefore, we obtain LCK or LCS structures on compact solvmanifolds (quotients of a Lie group by a lattice). Specifically we study LCK structures on solvmanifold where the complex structure is abelian. Then we describe the structure of a Lie algebra admitting a Vaisman structure. On the other hand we determine the almost abelian Lie groups equipped with a LCK or LCS structures, and we also analize the existence of lattices on these groups. Finally we construct a method to produce examples of Lie algebras admitting LCK or LCS structures beginning with a Lie algebra with these structures and a compatible representation.
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"The (n)-Solvable Filtration of the Link Concordance Group and Milnor's mu-Invariaants." Thesis, 2011. http://hdl.handle.net/1911/70379.
Full textAbstract:
We establish several new results about the ( n )-solvable filtration, [Special characters omitted.] , of the string link concordance group [Special characters omitted.] . We first establish a relationship between ( n )-solvability of a link and its Milnor's μ-invariants. We study the effects of the Bing doubling operator on ( n )-solvability. Using this results, we show that the "other half" of the filtration, namely [Special characters omitted.] , is nontrivial and contains an infinite cyclic subgroup for links with sufficiently many components. We will also show that links modulo (1)-solvability is a nonabelian group. Lastly, we prove that the Grope filtration, [Special characters omitted.] of [Special characters omitted.] is not the same as the ( n )-solvable filtration.
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Schneider, Jakob. "On the length of group laws." 2016. https://tud.qucosa.de/id/qucosa%3A36487.
Full textAbstract:
Let C be the class of finite nilpotent, solvable, symmetric, simple or semi-simple groups and n be a positive integer. We discuss the following question on group laws: What is the length of the shortest non-trivial law holding for all finite groups from the class C of order less than or equal to n?:Introduction
0 Essentials from group theory
1 The two main tools
1.1 The commutator lemma
1.2 The extension lemma
2 Nilpotent and solvable groups
2.1 Definitions and basic properties
2.2 Short non-trivial words in the derived series of F_2
2.3 Short non-trivial words in the lower central series of F_2
2.4 Laws for finite nilpotent groups
2.5 Laws for finite solvable groups
3 Semi-simple groups
3.1 Definitions and basic facts
3.2 Laws for the symmetric group S_n
3.3 Laws for simple groups
3.4 Laws for finite linear groups
3.5 Returning to semi-simple groups
4 The final conclusion
Index
BibliographySei C die Klasse der endlichen nilpotenten, auflösbaren, symmetrischen oder halbeinfachen Gruppen und n eine positive ganze Zahl. We diskutieren die folgende Frage über Gruppengesetze: Was ist die Länge des kürzesten nicht-trivialen Gesetzes, das für alle endlichen Gruppen der Klasse C gilt, welche die Ordnung höchstens n haben?:Introduction 0 Essentials from group theory 1 The two main tools 1.1 The commutator lemma 1.2 The extension lemma 2 Nilpotent and solvable groups 2.1 Definitions and basic properties 2.2 Short non-trivial words in the derived series of F_2 2.3 Short non-trivial words in the lower central series of F_2 2.4 Laws for finite nilpotent groups 2.5 Laws for finite solvable groups 3 Semi-simple groups 3.1 Definitions and basic facts 3.2 Laws for the symmetric group S_n 3.3 Laws for simple groups 3.4 Laws for finite linear groups 3.5 Returning to semi-simple groups 4 The final conclusion Index Bibliography