Dissertations / Theses: 'Group homomorphism'

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Slye, Jeffrey. "UNDERGRADUATE MATHEMATICS STUDENTS’ CONNECTIONS BETWEEN THEIR GROUP HOMOMORPHISM AND LINEAR TRANSFORMATION CONCEPT IMAGES." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/65.

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It is well documented that undergraduate students struggle with the more formal and abstract concepts of vector space theory in a first course on linear algebra. Some of these students continue on to classes in abstract algebra, where they learn about algebraic structures such as groups. It is clear to the seasoned mathematician that vector spaces are in fact groups, and so linear transformations are group homomorphisms with extra restrictions. This study explores the question of whether or not students see this connection as well. In addition, I probe the ways in which students’ stated understandings are the same or different across contexts, and how these differences may help or hinder connection making across domains. Students’ understandings are also briefly compared to those of mathematics professors in order to highlight similarities and discrepancies between reality and idealistic expectations. The data for this study primarily comes from clinical interviews with ten undergraduates and three professors. The clinical interviews contained multiple card sorts in which students expressed the connections they saw within and across the domains of linear algebra and abstract algebra, with an emphasis specifically on linear transformations and group homomorphisms. Qualitative data was analyzed using abductive reasoning through multiple rounds of coding and generating themes. Overall, I found that students ranged from having very few connections, to beginning to form connections once placed in the interview setting, to already having a well-integrated morphism schema across domains. A considerable portion of this paper explores the many and varied ways in which students succeeded and failed in making mathematically correct connections, using the language of research on analogical reasoning to frame the discussion. Of particular interest were the ways in which isomorphisms did or did not play a role in understanding both morphisms, how students did not regularly connect the concepts of matrices and linear transformations, and how vector spaces were not fully aligned with groups as algebraic structures.

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Hohlweg, Christophe. "Properties of the Solomon homomorphism of a finite Coxeter group and minimal elements in two-sided cells of the symmetric group." Université Louis Pasteur (Strasbourg) (1971-2008), 2003. http://www.theses.fr/2003STR13246.

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Caprace, Pierre-Emmanuel. ""Abstract" homomorphisms of split Kac-Moody groups." Doctoral thesis, Universite Libre de Bruxelles, 2005. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210962.

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Cette thèse est consacrée à une classe de groupes, appelés groupes de Kac-Moody, qui généralise de façon naturelle les groupes de Lie semi-simples, ou plus précisément, les groupes algébriques réductifs, dans un contexte infini-dimensionnel. On s'intéresse plus particulièrement au problème d'isomorphismes pour ces groupes, en vue d'obtenir un analogue infini-dimensionnel de la célèbre théorie des homomorphismes 'abstraits' de groupes algébriques simples, due à Armand Borel et Jacques Tits.

Le problème d'isomorphismes qu'on étudie s'avère être un cas particulier d'un problème plus général, qui consiste à caractériser les homomorphismes de groupes algébriques vers les groupes de Kac-Moody, dont l'image est bornée. Ce problème peut à son tour s'énoncer comme un problème de rigidité pour les actions de groupes algébriques sur les immeubles, via l'action naturelle d'un groupe de Kac-Moody sur une paire d'immeubles jumelés. Les résultats partiels, relatifs à ce problème de rigidité, que nous obtenons, nous permettent d'apporter une solution complète au problème d'isomorphismes pour les groupes de Kac-Moody déployés.

En particulier, on obtient un résultat de dévissage pour les automorphismes de ces objets. Celui-ci fournit à son tour une description complète de la structure du groupe d'automorphismes d'un groupe de Kac-Moody déployé sur un corps de caractéristique~$0$.

Nos arguments permettent également de traiter de façon analogue certaines formes anisotropes de groupes de Kac-Moody complexes, appelées formes unitaires. On montre en particulier que la topologie Hausdorff naturelle que portent ces formes est un invariant de leur structure de groupe abstrait. Ceci généralise un résultat bien connu de H. Freudenthal pour les groupes de Lie compacts.

Enfin, l'on s'intéresse aux homomorphismes de groupes de Kac-Moody à image fini-dimensionnelle, et l'on démontre la non-existence de tels homomorphismes à noyau central, lorsque le domaine est un groupe de Kac-Moody de type indéfini sur un corps infini. Ceci réduit un problème ouvert, dit problème de linéarité pour les groupes de Kac-Moody, au cas de corps de base finis.
Doctorat en sciences, Spécialisation mathématiques
info:eu-repo/semantics/nonPublished

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Nazzal, Lamies Joureus. "Homomorphic images of semi-direct products." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2770.

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The main purpose of this thesis is to describe methods of constructing computer-free proofs of existence of finite groups and give useful techniques to perform double coset enumeration of groups with symmetric presentations over their control groups.

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Torres, Giese Enrique. "Spaces of homomorphisms and group cohomology." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/224.

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In this work we study the space of group homomorphisms Hom(Γ,G) from a geometric and simplicial point of view. The case in which the source group is a free abelian group of rank n is studied in more detail since this space can be identified with the space of commuting n-tuples of elements from G. This latter case is of particular interest when the target is a Lie group. The simplicial approach allows us to to construct a family of spaces that filters the classifying space of a group by filtering group theoretical information of the given group. Namely, we use the lower central series of free groups to construct a family of simplicial subspaces of the bar construction of the classifying space of a group. The first layer of this filtration is studied in more detail for transitively commutative (TC) groups.

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Vera, Arboleda Anderson Arley. "Homomorphismes de type Johnson pour les surfaces et invariant perturbatif universel des variétés de dimension trois." Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAD009/document.

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Soit Σ une surface compacte connexe orientée avec une seule composante du bord. Notons par M le groupe d'homéotopie de Σ. En considérant l'action de M sur le groupe fondamental de Σ, il est possible de définir différentes filtrations de M ainsi que des homomorphismes sur chaque terme de ces filtrations. Le but de cette thèse est double. En premier lieu, nous étudions deux filtrations de M : la " filtration de Johnson-Levine " introduite par Levine et la " filtration de Johnson alternative " introduite recemment par Habiro et Massuyeau. Les définitions de ces deux filtrations prennent en compte un corps en anses bordé par la surface. Nous nous référons à ces filtrations comme " filtrations de type Johnson " et les homomorphismes correspondants sont appelés " homomorphismes de type Johnson " par leur analogie avec la filtration de Johnson originale et les homomorphismes de Johnson usuels. Nous donnons une comparaison de la filtration de Johnson avec la filtration de Johnson-Levine au niveau du monoïde des cobordismes d'homologie de Σ. Nous donnons également une comparaison entre la filtration de Johnson alternative, la filtration Johnson-Levine et la filtration de Johnson au niveau du groupe d'homéotopie. Deuxièmement, nous étudions la relation entre les " homomorphismes de type Johnson" et l'extension fonctorielle de l'invariant perturbatif universel des variétés de dimension trois (l'invariant de Le-Murakami-Ohtsuki ou invariant LMO). Cette extension fonctorielle s'appelle le foncteur LMO et il prend ses valeurs dans une catégorie de diagrammes. Nous démontrons que les "homomorphismes de type Johnson " peuvent être lus dans la réduction arborée du foncteur LMO. En particulier, cela fournit une nouvelle grille de lecture de la réduction arborée du foncteur LMO
Let Σ be a compact oriented surface with one boundary component and let M denote the mapping class group of Σ. By considering the action of M on the fundamental group of Σ it is possible to define different filtrations of M together with some homomorphisms on each term of the filtrations. The aim of this thesis is twofold. First, we study two filtrations of M : the « Johnson-Levine filtration » introduced by Levine and « the alternative Johsnon filtration » introduced recently by Habiro and Massuyeau. The definition of both filtrations involve a handlebody bounded by Σ. We refer to these filtrations as ≪ Johnson-type filtrations » and the corresponding homomorphisms have referred to as « Johnson-type homomorphisms » by their analogy with the original Johnson filtration and the usual Johnson homomorphisms. We provide a comparison of the Johnson filtration with the Johnson-Levine filtration at the level of the monoid of homology cobordisms of Σ. We also provide a comparison of the alternative Johnson filtration with the Johnson-Levine filtration and the Johnson filtration at the level of the mapping class group. Secondly, we study the relationship between the « Johnson-type homomorphisms » and the functorial extension of the universal perturbative invariant of 3-manifolds (the Le-Murakami-Ohtsuki invariant or LMO invariant). This functorial extension is calling the LMO functor and it takes values in a category of diagrams. We prove that the « Johnson-type homomorphisms » is in the tree reduction of the LMO functor. In particular, this provides a new reading grid of the tree reduction of the LMO functor

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Baccari, Angelica. "Simple Groups, Progenitors, and Related Topics." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/736.

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The foundation of the work of this thesis is based around the involutory progenitor and the finite homomorphic images found therein. This process is developed by Robert T. Curtis and he defines it as 2^{*n} :N {pi w | pi in N, w} where 2^{*n} denotes a free product of n copies of the cyclic group of order 2 generated by involutions. We repeat this process with different control groups and a different array of possible relations to discover interesting groups, such as sporadic, linear, or unitary groups, to name a few. Predominantly this work was produced from transitive groups in 6,10,12, and 18 letters. Which led to identify some appealing groups for this project, such as Janko group J1, Symplectic groups S(4,3) and S(6,2), Mathieu group M12 and some linear groups such as PGL2(7) and L2(11) . With this information, we performed double coset enumeration on some of our findings, M12 over L_2(11) and L_2(31) over D15. We will also prove their isomorphism types with the help of the Jordan-Holder theorem, which aids us in defining the make up of the group. Some examples that we will encounter are the extensions of L_2(31)(center) 2 and A5:2^2.

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Kent, Curtis Andrew. "Homomorphisms into the Fundamental Group of One-Dimensional and Planar Peano Continua." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2452.pdf.

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9

Farber, Lee. "Symmetric generation of finite homomorphic images?" CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2901.

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The purpose of this thesis was to present the technique of double coset enumeration and apply it to construct finite homomorphic images of infinite semidirect products. Several important homomorphic images include the classical groups, the Projective Special Linear group and the Derived Chevalley group were constructed.

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10

Peim, M. D. "On the K-theory and homotopy groups of #OMEGA# #SIGMA#BU." Thesis, University of Manchester, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257661.

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Yoo, Jane. "Construction of finite homomorphic images." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3196.

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Manriquez, Adam. "Symmetric Presentations, Representations, and Related Topics." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/711.

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The purpose of this thesis is to develop original symmetric presentations of finite non-abelian simple groups, particularly the sporadic simple groups. We have found original symmetric presentations for the Janko group J1, the Mathieu group M12, the Symplectic groups S(3,4) and S(4,5), a Lie type group Suz(8), and the automorphism group of the Unitary group U(3,5) as homomorphic images of the progenitors 2*60 : (2 x A5), 2*60 : A5, 2*56 : (23 : 7), and 2*28 : (PGL(2,7):2), respectively. We have also discovered the groups 24 : A5, 34 : S5, PSL(2,31), PSL(2,11), PSL(2,19), PSL(2,41), A8, 34 : S5, A52, 2• A52, 2 : A62, PSL(2,49), 28 : A5, PGL(2,19), PSL(2,71), 24 : A5, 24 : A6, PSL(2,7), 3 x PSL(3,4), 2• PSL(3,4), PSL(3,4), 2• (M12 : 2), 37:S7, 35 : S5, S6, 25 : S6, 35 : S6, 25 : S5, 24 : S6, and M12 as homomorphic images of the permutation progenitors 2*60 : (2 x A5), 2*60 : A5, 2*21 : (7: 3), 2*60 : (2 x A5), 2*120 : S5, and 2*144 : (32 : 24). We have given original proof of the 2*n Symmetric Presentation Theorem. In addition, we have also provided original proof for the Extension of the Factoring Lemma (involutory and non-involutory progenitors). We have constructed S5, PSL(2,7), and U(3,5):2 using the technique of double coset enumeration and by way of linear fractional mappings. Furthermore, we have given proofs of isomorphism types for 7 x 22, U(3,5):2, 2•(M12 : 2), and (4 x 2) :• 22.

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V, Budimirović Branka. "Mrežno vrednosni identiteti i neke klase mrežno vrednosnih podalgebri." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2011. https://www.cris.uns.ac.rs/record.jsf?recordId=77334&source=NDLTD&language=en.

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Neka je A neprazan skup i L = (L;·) proizvoljna mreža sa nulom i jedinicom. Svako preslikavanje A¯ : A ¡! L zovemo rasplinuti podskup od A. Uobičajeno je da se rasplinute podgrupe definišu na grupi. U radu su fazi podgrupe definisane na polugrupi kao i na rasplinutoj podpolugrupi. Jedan od glavnih rezultata je teorema o particiji rasplinutih kompletno regularnih polugrupa. Takođe su definisane rasplinute kongruencije i rasplinute jednakosti na rasplinutim podalgebrama neke algebre i ispitane njihove osobine. Uvedeni su pojmovi: podalgebre rasplinute podalgebre, rasplinutog homomorfizma rasplinute podalgebre na rasplinutu podalgebru i direktnog proizvoda rasplinutih podalgebri. Jedan od važnijih rezultata je teorema koja je uopštenje teoreme Birkhoff-a na rasplinutim strukturama.
Let A be nonemptu set, and let L = (L; 6) be a lattice with 0 and 1. The mapping A¯ : A ! L is called fuzzy subset of A. It is usual to define fuzzy subgroup on the group. In this work fuzzy semigroups are defined on the semigroup and on the fuzzy subsemigroup, too. As a main result is theorem about partition fuzzy completlu regular semigroup. Also, fuzzy congruences are defined, and fuzzy equolites on fuzzy subalgebras of an algebra and their propertes are investigated. We introduced some new notions: subalgebras of fuzzy subalgebras, fuzzy homomorphism of fuzzy subalgebra, and direct product of fuzzy subalgebras. One of the most important result is extension of Birkhoff’s theorem on fuzzy structures.

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Bernhardt, Karen 1977. "The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/28922.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 73-74).
For complex reductive Lie algebras g, the classical Harish-Chandra homomorphism allows to link irreducible finite dimensional representations of g to those of certain subalgebras l. The Casselman-Osborne theorem establishes an extension of this link to infinite dimensional irreducible representations. In this paper we present a generalized Harish-Chandra homomorphism construction for Hecke algebras, and establish the corresponding generalized Casselman-Osborne theorem. This homomorphism can be used to link representations of (g, L n K)-pairs to those of (g, L n K)-pairs, where is a certain subalgebra of g as in the classical case. Since representations of such pairs are closely related to those of the underlying Lie group G, this construction is a good first approximation to lifting the Harish-Chandra homomorphism from the Lie algebra to the Lie group level.
by Karen Bernhardt.
S.M.

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Konstantinou, Panagiota. "Homomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the Mapping Class Group." Diss., Tucson, Arizona : University of Arizona, 2006. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu%5Fetd%5F1653%5F1%5Fm.pdf&type=application/pdf.

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Doherty, Conor J. "Canonical solution groups of a homomorphism : manipulator kinematics, nonparametric regression and distributed object systems." Thesis, Aston University, 1997. http://publications.aston.ac.uk/7973/.

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The kinematic mapping of a rigid open-link manipulator is a homomorphism between Lie groups. The homomorphisrn has solution groups that act on an inverse kinematic solution element. A canonical representation of solution group operators that act on a solution element of three and seven degree-of-freedom (do!) dextrous manipulators is determined by geometric analysis. Seven canonical solution groups are determined for the seven do! Robotics Research K-1207 and Hollerbach arms. The solution element of a dextrous manipulator is a collection of trivial fibre bundles with solution fibres homotopic to the Torus. If fibre solutions are parameterised by a scalar, a direct inverse funct.ion that maps the scalar and Cartesian base space coordinates to solution element fibre coordinates may be defined. A direct inverse pararneterisation of a solution element may be approximated by a local linear map generated by an inverse augmented Jacobian correction of a linear interpolation. The action of canonical solution group operators on a local linear approximation of the solution element of inverse kinematics of dextrous manipulators generates cyclical solutions. The solution representation is proposed as a model of inverse kinematic transformations in primate nervous systems. Simultaneous calibration of a composition of stereo-camera and manipulator kinematic models is under-determined by equi-output parameter groups in the composition of stereo-camera and Denavit Hartenberg (DH) rnodels. An error measure for simultaneous calibration of a composition of models is derived and parameter subsets with no equi-output groups are determined by numerical experiments to simultaneously calibrate the composition of homogeneous or pan-tilt stereo-camera with DH models. For acceleration of exact Newton second-order re-calibration of DH parameters after a sequential calibration of stereo-camera and DH parameters, an optimal numerical evaluation of DH matrix first order and second order error derivatives with respect to a re-calibration error function is derived, implemented and tested. A distributed object environment for point and click image-based tele-command of manipulators and stereo-cameras is specified and implemented that supports rapid prototyping of numerical experiments in distributed system control. The environment is validated by a hierarchical k-fold cross validated calibration to Cartesian space of a radial basis function regression correction of an affine stereo model. Basic design and performance requirements are defined for scalable virtual micro-kernels that broker inter-Java-virtual-machine remote method invocations between components of secure manageable fault-tolerant open distributed agile Total Quality Managed ISO 9000+ conformant Just in Time manufacturing systems.

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Simard, Nicolas. "The Mazur-Tate pairing and explicit homomorphisms between Mordell-Weil groups of elliptic curves and ideal class groups." Thesis, McGill University, 2014. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=123330.

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In [Buell(1977)] and [Soleng(1994)], Buell and Soleng found explicit homomorphismsbetween the Mordell-Weil group of elliptic curves and the ideals class group of quadraticelds, which turn out to be essentially equivalent. After recalling the basic conceptsin the theories of quadratic forms, quadratic elds and elliptic curves, we prove thatSoleng's homomorphism can be obtained via a height pairing introduced by Mazur andTate [Mazur and Tate(1983)], under certain conditions. Then the technique developed inthe proof of this result is used to nd new homomorphisms. Examples of explicit computationsof the Mazur-Tate pairing are also given.
Dans les articles [Buell(1977)] et [Soleng(1994)], Buell et Soleng mettent en évidencedes homomorphismes explicites entre le groupe de Mordell-Weil des courbes elliptiques etle groupe des classes d'idéaux des corps quadratiques. Après avoir introduit les théories desformes quadratiques, des corps quadratiques et des courbes elliptiques, il sera démontré quel'homomorphisme de Soleng, qui est essentiellement équivalent à celui de Buell, peut êtreobtenu à l'aide d'un accouplement de hauteur dû à Mazur et Tate [Mazur and Tate(1983)].Par la suite, les idées rencontrées dans la preuve de ce résultat seront utilisées pour découvrirde nouveaux homomorphismes. Des exemples de calculs explicites de l'accouplement deMazur-Tate sont aussi donnés.

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Marouf, Manal Abdulkarim Ms. "Simple Groups and Related Topics." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/239.

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In this thesis, we will give our discovery of original symmetric presentations of several important groups. We have investigated permutation and monomial progenitors 2*8: (23: 22), 2*9: (32: 24), 2*10: (24: (2 × 5)), 5*4:m (23: 22), 7*8:m (32: 24), and 3*5:m (24: (2 × 5)). The finite images of the above progenitors include the Mathieu sporadic group M12, the linear groups L2(8) and L2(13), and the extensions S6 × 2, 28 : .L2(8) , and 27 : .A5. We will show our construction of the four groups S3 , L2(8), L2(13), and S6 × 2 over S3, 22, S3 : 2, and S5, by using the technique of double coset enumeration. We will also provide isomorphism types all of the groups that have appeared as finite homomorphic images. We will show that the group L2(8) does not satisfy the conditions of Iwasawas Lemma and that the group L2(13) is simple by Iwasawas Lemma. We give constructions of M22 × 2 and M22 as homomorphic images of the progenitor S6.

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Lamp, Leonard B. "SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/222.

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The goal of this thesis is to show constructions of some of the sporadic groups such as the Mathieu group, M12, J1, Projective Special Linear groups, PSL(2,8), and PSL(2,11), Unitary group U(3,3) and many other non-abelian simple groups. Our purpose is to find all simple non-abelian groups as homomorphic images of permutation or monomial progenitors, as well grasping a deep understanding of group theory and extension theory to determine groups up to isomorphisms. The progenitor, developed by Robert T. Curtis, is a semi-direct product of the following form: P≅2*n: N = {πw | π ∈ N, w a reduced word in the ti} where 2*n denotes a free product of n copies of the cyclic group of order 2 generated by involutions ti for 1 ≤ i≤ n; and N is a transitive permutation group of degree n which acts on the free product by permuting the involuntary generators by conjugation. Thus we develop methods for factoring by a suitable any number of relations in the hope of finding all non-abelian simple groups, and in particular one of the 26 Sporadic simple groups. Then the algorithm for double coset enumeration together with the first isomorphic theorem aids us in proving the homomorphic image of the group we have constructed. After being presented with a group G, we then compute the composition series to solve extension problems. Given a composition such as G = G0 ≥ G1 ≥ ….. ≥ Gn-1 ≥ Gn = 1 and the corresponding factor groups G0/G1 = Q1,…,Gn-2/Gn-1 = Qn-1,Gn-1/Gn = Qn. We note that G1 = 1, implying Gn-1 = Qn. As we move through the next composition factor we see that Gn-2/Qn = Qn-1, so that Gn-2 is an extension of Qn-1 by Qn. Following this procedure we can recapture G from the products of Qi and thus solve the extension problem. The Jordan-Holder theorem then allows us to develop a process to analyze all finite groups if we knew all finite simple groups and could solve their extension problem, hence arriving at the isomorphism type of the group. We will present how we solve extensions problems while our main focus will lie on extensions that will include the following: semi-direct products, direct products, central extensions and mixed extensions.Lastly, we will discuss Iwasawa's Lemma and how double coset enumeration aids us in showing the simplicity of some of our groups.

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Zeng, William J. "The abstract structure of quantum algorithms." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:cace8fba-b533-42f7-b9fd-959f2412c2a7.

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Quantum information brings together theories of physics and computer science. This synthesis challenges the basic intuitions of both fields. In this thesis, we show that adopting a unified and general language for process theories advances foundations and practical applications of quantum information. Our first set of results analyze quantum algorithms with a process theoretic structure. We contribute new constructions of the Fourier transform and Pontryagin duality in dagger symmetric monoidal categories. We then use this setting to study generalized unitary oracles and give a new quantum blackbox algorithm for the identification of group homomorphisms, solving the GROUPHOMID problem. In the remaining section, we construct a novel model of quantum blackbox algorithms in non-deterministic classical computation. Our second set of results concerns quantum foundations. We complete work begun by Coecke et al., definitively connecting the Mermin non-locality of a process theory with a simple algebraic condition on that theory's phase groups. This result allows us to offer new experimental tests for Mermin non-locality and new protocols for quantum secret sharing. In our final chapter, we exploit the shared process theoretic structure of quantum information and distributional compositional linguistics. We propose a quantum algorithm adapted from Weibe et al. to classify sentences by meaning. The clarity of the process theoretic setting allows us to recover a speedup that is lost in the naive application of the algorithm. The main mathematical tools used in this thesis are group theory (esp. Fourier theory on finite groups), monoidal category theory, and categorical algebra.

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Grindstaff, Dustin J. "Symmetric Presentations and Generation." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/202.

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The aim of this thesis is to generate original symmetric presentations for finite non-abelian simple groups. We will discuss many permutation progenitors, including but not limited to 2*14 : D28, 2∗9 : 3•(32), 3∗9 : 3•(32), 2∗21 : (7X3) : 2 as well as monomial progenitors, including 7∗5 :m A5, 3∗5 :m S5. We have included their homomorphic images which include the Mathieu group M12, 2•J2, 2XS(4, 5), as well as, many PGL′s, PSL′s and alternating groups. We will give proofs of the isomorphism types of each progenitor, either by hand using double coset enumeration or computer based using MAGMA. We have also constructed Cayley graphs of the following groups, 25 : S5 over 2∗5 : S5, PSL(2, 8) over 2∗7 : D14, M12 over a maximal subgroup, 2XS5. We have developed a lemma using relations to factor permutation progenitors of the form m∗n : N to give an isomorphism of mn : N . Motivated by Robert T. Curtis’ research, we will present a program using MAGMA that, when given a target finite non-abelian simple group, the program will generate possible control groups to write progenitors that will give the given finite non-abelian simple group. Iwasawa’s lemma is also discussed and used to prove PSL(2, 8) and M12 to be simple groups.

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Berger, Clemens. "Une version effective du théorème de Hurewicz." Phd thesis, Grenoble 1, 1991. http://tel.archives-ouvertes.fr/tel-00339314.

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Daniel Kan associe a tout ensemble simplicial réduit x un fibre principal contractile de base x et de fibre un groupe simplicial libre, note gx. Un concept généralisé de prisme nous permet de considérer ce groupe comme sous-quotient canonique d'un modèle simplicial de l'espace de lacets de x, et de munir l'espace total du fibre d'une contraction combinatoire évoquant l'idée topologique de contraction des chemins. Est ainsi établie une correspondance biunivoque explicite entre les représentants algébriques des classes d'homotopie de Gx et certains représentants géométriques des classes d'homotopie de x. En utilisant les propriétés homotopiques du commutant de Gx nous obtenons enfin une version effective du théorème de Hurewicz comportant entre autres la construction algorithmique de sphères combinatoires a partir de certains cycles homologique

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Auclair, Emmanuel. "Les Surfaces et invariants de type fini en dimension 3." Phd thesis, Université Joseph Fourier (Grenoble), 2006. http://tel.archives-ouvertes.fr/tel-00113863.

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Cette thèse porte sur les invariants des sphères d'homologie entière de dimension 3, et en particulier sur les invariants de type fini pour la filtration de Goussarov-Habiro.
Dans une première partie, on étudie la variation d'un invariant de degré 2n après chirurgie le long d'une surface par un élément du 2n-ième terme de la série centrale descendante du groupe de Torelli. Dans le cas d'un commutateur de 2n éléments du groupe de Torelli, on exprime cette variation en fonction de l'homomorphisme de Johnson évalué sur ces 2n éléments et du système de poids de l'invariant.

Le calcul des claspers de Goussarov-Habiro donne des équivalences topologiques entre des chirurgies sur des corps en anses plongés dans les variétés. Ce calcul a déjà permis de préciser le comportement des invariants de type fini lors de nombreuses modifications topologiques. La deuxième partie de cette thèse est consacrée à un raffinement de ce calcul. Ce raffinement est ensuite appliqué à l'obtention d'une formule de chirurgie géométrique sur les noeuds pour les invariants de degré 4, c'est-à-dire que l'on exprime la variation d'un tel invariant après chirurgie sur un noeud en fonction d'invariants de courbes tracées au voisinage d'une surface de Seifert de ce noeud.

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24

Hendtlass, Matthew. "Aspects of constructive dynamical systems : a thesis submitted in partial fulfilment of the requirements of the degree for Master of Science in Mathematics at the University of Canterbury /." 2009. http://hdl.handle.net/10092/2724.

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25

Chen, Shin-I., and 陳欣宜. "The torsion-free homomorphic images of completely decomposable groups with rank-1 kernels." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/70489537663476204111.

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碩士
淡江大學
數學學系
85
Let $A=(A_1,A_2,...,A_n) $ be a co-doubly incomparable n-tuple of subgroups the class of Butler groups that are isomorphic to $G[A] = (A_1 \oplus \cdots\oplus A_n) / \langle (a,...,a) \rangle _* $, where $0 \ne a \in \cap A_i $. We construct two quantities, the first is a set of types $\overline{T}_A $; the second is a matrix $\overline{E}_A $ of integers and symbols $- \infty $,whose columns are indexed by $ \overline{T}_A $ and whose rows are indexed by the primes. The set $\overline{T}_A $ is a complete set of invariants for$ G[A] $ under quasi-isomorphism (Theorem 3.4). The matrix $ \overline{E}_A $is determined by $\overline{T}_A $ up to a finite number of entries, and together with $\overline{T}_A $ forms a complete set of invariants for$G[A] $ under isomorphism (Theorem 3.4, 4.1, and 4.3). Let $A $ and $B $ be n-tuples of subgroups of $Q $. Call $A $ and $B $ equivalent if they can be made equal via a succession of supplementing,permutations, and scalar multiplications. We show that the following three conditions are equivalent if $A $ and $B $ are co-doubly incomparable : (1) $A $ is equivalent to $B $, (2) $G[A] $ is isomorphic $G[B] $, (3) $ \overline{T}_A $ = $\overline{T}_B $, $\overline{E}_A $ = $\overline{E}_B $.

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26

Hamouda, Hawa. "Modules maps and Invariant subsets of Banach modules of locally compact groups." 2013. http://hdl.handle.net/1993/17598.

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For a locally compact group G, the papers [13] and [7] have many results about G-invariant subsets of G-modules, and the relationship between G-module maps, L1(G)-module maps and M(G)-module maps. In both papers, the results were given for one specific module action. In this thesis we extended many of their results to arbitrary Banach G-modules. In addition, we give detailed proofs of most of the results found in the first section of the paper [21].

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27

Fournier, J. "Automorphismes et isomorphismes des graphes de Cayley." Thèse, 2004. http://hdl.handle.net/1866/17274.

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Dissertations / Theses on the topic 'Group homomorphism'

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