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Dissertations / Theses on the topic 'Group theory'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Isenrich, Claudio Llosa. "Kähler groups and Geometric Group Theory." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:4a7ab097-4de5-4b72-8fd6-41ff8861ffae.

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In this thesis we study Kähler groups and their connections to Geometric Group Theory. This work presents substantial progress on three central questions in the field: (1) Which subgroups of direct products of surface groups are Kähler? (2) Which Kähler groups admit a classifying space with finite (n-1)-skeleton but no classifying space with finitely many n-cells? (3) Is it possible to give explicit finite presentations for any of the groups constructed in response to Question 2? Question 1 was raised by Delzant and Gromov. Question 2 is intimately related to Question 1: the non-trivial exa

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2

Griffin, Cornelius John. "Subgroups of infinite groups : interactions between group theory and number theory." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252018.

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3

Coutts, Hannah Jane. "Topics in computational group theory : primitive permutation groups and matrix group normalisers." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2561.

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Part I of this thesis presents methods for finding the primitive permutation groups of degree d, where 2500 ≤ d < 4096, using the O'Nan-Scott Theorem and Aschbacher's theorem. Tables of the groups G are given for each O'Nan-Scott class. For the non-affine groups, additional information is given: the degree d of G, the shape of a stabiliser in G of the primitive action, the shape of the normaliser N in S[subscript(d)] of G and the rank of N. Part II presents a new algorithm NormaliserGL for computing the normaliser in GL[subscript(n)](q) of a group G ≤ GL[subscript(n)](q). The algorithm is impl

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4

Martin, Michael Patrick McAlarnen. "Computational Group Theory." Thesis, The University of Arizona, 2015. http://hdl.handle.net/10150/579297.

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The study of finite groups has been the subject of much research, with substantial success in the 20th century, in part due to the development of representation theory. Representation theory allows groups to be studied using the well-understood properties of linear algebra, however it requires the researcher to supply a representation of the group. One way to produce representations of groups is to take a representation of a subgroup and use it to induce a representation. We focus on the finite simple groups because they are the buliding blocks of an arbitrary simple group. This thesis investi

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5

Garotta, Odile. "Suites presque scindées d'algèbres intérieures et algèbres intérieures des suites presque scindées." Paris 7, 1988. http://www.theses.fr/1988PA077184.

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Dans le cadre de l'etude des representations modulaires d'un groupe fini sur un corps, nous generalisons la notion, introduite par auslander et reiten, de "suite exacte presque scindee" de nodules (sur l'algebre de groupe), en une notion de "systemes d'idempotents" (dits systemes de auslander-reiten) dans une algebre "interieure" (du point de vue de l'operation du groupe) symetrique quelconque. Raisonnant a l'interieur des algebres, nous donnons, comme dans la theorie classique, un resultat d'"existence et unicite" des systemes de auslander-reiten. D'autre part le point de vue de l'"algebre co

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6

McSorley, J. P. "Topics in group theory." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376929.

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7

Hegedüs, Pál. "Topics in group theory." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620412.

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8

Colletti, Bruce William. "Group theory and metaheuristics /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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9

Menezes, Nina E. "Random generation and chief length of finite groups." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3578.

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Part I of this thesis studies P[subscript(G)](d), the probability of generating a nonabelian simple group G with d randomly chosen elements, and extends this idea to consider the conditional probability P[subscript(G,Soc(G))](d), the probability of generating an almost simple group G by d randomly chosen elements, given that they project onto a generating set of G/Soc(G). In particular we show that for a 2-generated almost simple group, P[subscript(G,Soc(G))](2) 53≥90, with equality if and only if G = A₆ or S₆. Furthermore P[subscript(G,Soc(G))](2) 9≥10 except for 30 almost simple groups G, an

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10

Cornwell, Christopher R. "On the Combinatorics of Certain Garside Semigroups." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1381.pdf.

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11

Semikina, Iuliia [Verfasser]. "G-theory of group rings for finite groups / Iuliia Semikina." Bonn : Universitäts- und Landesbibliothek Bonn, 2018. http://d-nb.info/1173789642/34.

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12

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 f<sub>φ</sub>(p<sup>m</sup>) to be the number of (isomorphism classes of) groups of order p<sup>m</sup> 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

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13

Peterson, Aaron. "Pipe diagrams for Thompson's Group F /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1959.pdf.

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14

Evans, D. M. "Some topics in group theory." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355748.

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15

Benson, Martin. "Topics in geometric group theory." Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.428957.

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16

Lerch, Brian A. "Theory of Social Group Dynamics." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1558361571474294.

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17

Martin, Stuart. "Quivers and the modular representation theory of finite groups." Thesis, University of Oxford, 1988. http://ora.ox.ac.uk/objects/uuid:59d4dc72-60e5-4424-9e3c-650eb2b1d050.

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The purpose of this thesis is to discuss the rôle of certain types of quiver which appear in the modular representation theory of finite groups. It is our concern to study two different types of quiver. First of all we construct the ordinary quiver of certain blocks of defect 2 of the symmetric group, and then apply our results to the alternating group and to the theory of partitions. Secondly, we consider connected components of the stable Auslander-Reiten quiver of certain groups G with normal subgroup N. The main interest lies in comparing the tree class of components of N-modules, with the

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18

Alp, Murat. "GAP, crossed inodules, Cat'1-groups : applications of computational group theory." Thesis, Bangor University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361168.

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19

Carette, Mathieu. "The automorphism group of accessible groups and the rank of Coxeter groups." Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210261.

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Cette thèse est consacrée à l'étude du groupe d'automorphismes de groupes agissant sur des arbres d'une part, et du rang des groupes de Coxeter d'autre part.<p><p>Via la théorie de Bass-Serre, un groupe agissant sur un arbre est doté d'une structure algébrique particulière, généralisant produits amalgamés et extensions HNN. Le groupe est en fait déterminé par certaines données combinatoires découlant de cette action, appelées graphes de groupes. <p><p>Un cas particulier de cette situation est celle d'un produit libre. Une présentation du groupe d'automorphisme d'un produit libre d'un nombre fi

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20

Bajpai, Jitendra. "Omnipotence of surface groups." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=100245.

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Roughly speaking, a group G is omnipotent if orders of finitely many elements can be controlled independently in some finite quotients of G. We proved that pi1(S) is omnipotent when S is a surface other than P2,T2 or K2 . This generalizes the fact, previously known, that free groups are omnipotent. The proofs primarily utilize geometric techniques involving graphs of spaces with the aim of retracting certain spaces onto graphs.<br>Approximativement, on peut dire qu'un groupe G est omnipotent si les ordresquantité d'élements d'une quantite finie d'elements peuvent etre controles independamment

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21

Giroux, Yves. "Degenerate enveloping algebras of low-rank groups." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74026.

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22

Miyazaki, Takunari. "Polynomial-time computation in matrix groups /." view abstract or download file of text, 2000. http://wwwlib.umi.com/cr/uoregon/fullcit?p9955920.

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Thesis (Ph. D.)--University of Oregon, 2000.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 89-93). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9955920.

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23

Silberstein, Aaron. "Anabelian Intersection Theory." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10141.

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Let F be a field finitely generated and of transcendence degree 2 over \(\bar{\mathbb{Q}}\). We describe a correspondence between the smooth algebraic surfaces X defined over \(\bar{\mathbb{Q}}\) with field of rational functions F and Florian Pop’s geometric sets of prime divisors on \(Gal(\bar{F}/F)\), which are purely group-theoretical objects. This allows us to give a strong anabelian theorem for these surfaces. As a corollary, for each number field K, we give a method to construct infinitely many profinite groups \(\Gamma\) such that \(Out_{cont} (\Gamma)\) is isomorphic to \(Gal(\bar{K}/K

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24

Helffer, B., M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, N. Nadirashvili, and thoffman@esi ac at. "Spectral Theory for the Dihedral Group." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1018.ps.

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25

Grenham, Dermot. "Some topics in nilpotent group theory." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329954.

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26

Castaneda, Maria de los Dolores Sanchez. "Group Decision Making : Theory and Applications." Thesis, University of Kent, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.499771.

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27

Pridham, Jonathan Paul. "Deformation theory and the fundamental group." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616259.

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28

Haßler, Falk. "Double field theory on group manifolds." Diss., Ludwig-Maximilians-Universität München, 2015. http://nbn-resolving.de/urn:nbn:de:bvb:19-184273.

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This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. All observables arising from those dynamics match on certain families of background space times. These different backgrounds are connected by T-duality. DFT renders T-duality on a torus manifest by adding D windig coordinates in addition to the D space time coordinates. An essential consistency constraint of the theory, the strong constraint, only allows for fields which depend on half of the coordinates of the arising doubled space. An important applic

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29

Mehanna, M. A.-H. "Some computational problems in group theory." Thesis, University of Liverpool, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384569.

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30

Williams, Benjamin Thomas. "Two topics in geometric group theory." Thesis, University of Southampton, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323942.

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31

Al-Amri, Ibrahim Rasheed. "Computational methods in permutation group theory." Thesis, University of St Andrews, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636485.

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In Chapters 2 and 3 of this thesis, we find the structure of all groups generated by an n-cycle and a 2-cycle or a 3-cycle. When these groups fail to be either Sn or An then we show that they form a certain wreath product or an extension of a wreath product. We also determine, in Chapters 4 and 5, the structure of all groups generated by an n-cycle and the product of two 2-cycles or a 4-cycle. The structure of these groups depends on the results obtained in the previous chapters. In Chapter 6 we give some general results of groups generated by an n-cycle and a k-cycle. In Chapter 7 we calculat

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32

Eberhard, Sean. "Some combinatorial problems in group theory." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:b92af6aa-df2a-4634-882d-236d8f828857.

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We study a number of problems of a group-theoretic origin or nature, but from a strongly additive-combinatorial or analytic perspective. Specifically, we consider the following particular problems. 1. Given an arbitrary set of n positive integers, how large a subset can you be sure to find which is sum-free, i.e., which contains no two elements x and y as well as their sum x+y? More generally, given a linear homogeneous equation E, how large a subset can you be sure to find which contains no solutions to E? 2. Given a finite group G, suppose we measure the degree of abelianness of G by its com

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33

Gordon, Iain. "Representation theory of quantised function algebras at roots of unity." Thesis, Connect to electronic version, 1998. http://hdl.handle.net/1905/177.

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34

Gill, Olivia Jo. "Geometric and homological methods in group theory : constructing small group resolutions." Thesis, London Metropolitan University, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.573402.

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Given two groups K and H for which we have the free crossed resolutions, B* ɛ K and C* ɛ H respectively. Our aim is to construct a free crossed resolution, A* ɛ G, by way of induction on the degree n, for any semidirect product G = K ><I H. First we show how to find a set ZI of generators for the free group Al and the corresponding unique epimorphism from the free group on those generators to the semidirect product. This gives us the l-dimensional free crossed resolution A1 ɛ G, (see Proposition 4.1). Next we define a set of generators Z2 that together with Z1, constitute a gener- ating se

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35

Simeonov, Dimitar. "Essays in Contest Theory:." Thesis, Boston College, 2020. http://hdl.handle.net/2345/bc-ir:108933.

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Thesis advisor: Hideo Konishi<br>The majority of this work focuses on the theoretical analysis of collective action, group efficiency, and incentive mechanisms in team contests where individual outlays of heterogeneous agents are not observable. The reward allocation within the group is instead dependent on observable worker characteristics, modeled as individual abilities, as well as on the observable level of aggregate output. I study the incentives for free-riding and the group-size paradox under a very general set of intra-team allocation rules. I further derive the optimal allocation mech

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36

Cosgrove, Kenneth Mark. "The tangled web : ethnic groups, interest group theory, and congressional foreign policymaking /." Full-text version available from OU Domain via ProQuest Digital Dissertations, 1993.

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37

Eyl, Jennifer S. "Spanning subsets of a finite abelian group of order pq /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/eylj/jennifereyl.pdf.

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38

邵慰慈 and Wai-chee Shiu. "The algebraic structure and computation of Schur rings." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1992. http://hub.hku.hk/bib/B31233181.

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39

Shiu, Wai-chee. "The algebraic structure and computation of Schur rings /." [Hong Kong : University of Hong Kong], 1992. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1329037X.

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40

Catanzaro, Alessio. "Random matrix theory and renormalization group: spectral theory for network ensembles." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20547/.

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In this thesis we tackle the issue of spectral properties of networks introduced by Complex Systems Physics. Graph theory has developed methods to study the spectral properties of adjacency or stochastic matrices associated to networks based on algebraic techniques, whereas the applications to Complex Systems Theory have been essentially based on the methods of Statistical Mechanics. We use an approach to the problem using the results of the RMT in connection with some statistical mechanics techniques. RMT is of use in clarifying the physical meaning of Wigner law for large, random networks,

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41

Nicholson, Julia. "Otto HoÌˆlder and the development of group theory and Galois theory". Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333485.

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42

Bleak, Collin. "Solvability in groups of piecewise-linear homeomorphisms of the unit interval." Diss., Online access via UMI:, 2005.

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43

Ramsay, Denise. "On linearly ordered sets and permutation groups of uncountable degree." Thesis, University of Oxford, 1990. http://ora.ox.ac.uk/objects/uuid:ce9a8b26-bb4c-4c85-8231-78e89ce4109d.

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In this thesis a set, Ω, of cardinality N<sub>K</sub> and a group acting on Ω, with N<sub>K+1</sub> orbits on the power set of Ω, is found for every infinite cardinal N<sub>K</sub>. Let W<sub>K</sub> denote the initial ordinal of cardinality N<sub>K</sub>. Define N := {α<sub>1</sub>α<sub>2</sub> . . . α<sub>n</sub>∣ 0 < n < w, α<sub>j</sub> ∈ w<sub>K</sub> for j = 1, . . .,n, α<sub>n</sub> a successor ordinal} R := {ϰ ∈ N ∣ length(ϰ) = 1 mod 2} and let these sets be ordered lexicographically. The order types of N and R are Κ-types (countable unions of scattered types) which have cardinality N<

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44

Harkins, Andrew. "Combining lattices of soluble lie groups." Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341777.

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45

Moore, Monty L. "On Groups of Positive Type." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc277804/.

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We describe groups of positive type and prove that a group G is of positive type if and only if G admits a non-trivial partition. We completely classify groups of type 2, and present examples of other groups of positive type as well as groups of type zero.

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46

Bernstein, Brett David. "Higher natural numbers and omega words." Diss., Online access via UMI:, 2005.

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47

Richardson, Nela N. Thomas. "An interest group theory of financial development." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2950.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.<br>Thesis research directed by: Economics. 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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48

Hekmati, Pedram. "Group Extensions, Gerbes and Twisted K-theory." Licentiate thesis, Stockholm : Teoretisk fysik, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4654.

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49

Sklinos, Rizos. "Some model theory of the free group." Thesis, University of Leeds, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545716.

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50

Ashdown, M. A. J. "Geometric algebra, group theory and theoretical physics." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596181.

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This dissertation applies the language of geometric algebra to group theory and theoretical physics. Geometric algebra, which is introduced in Chapter 2, provides a natural extension of the concept of multiplication from real numbers to geometric objects such as line segments and planes. It is based on Clifford algebra and augmented by auxiliary definitions which give it a geometric interpretation. Since geometric algebra provides a natural encoding of the concepts of directed quantities, it has the potential to unify many of the disparate systems of notation that are used in mathematics. In C

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