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Dissertations / Theses on the topic 'Group theory'

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Published: 4 June 2021

Last updated: 9 June 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 examples of Kähler subgroups of direct products of surface groups never admit a classifying space with finite skeleton. The only known source of non-trivial examples for Questions 1 and 2 are fundamental groups of fibres of holomorphic maps from a direct product of closed surfaces onto an elliptic curve; the first such construction is due to Dimca, Papadima and Suciu. Question 3 was posed by Suciu in the context of these examples. In this thesis we: provide the first constraints on Kähler subdirect products of surface groups (<strong>Theorem 7.3.1</strong>); develop new construction methods for Kähler groups from maps onto higher-dimensional complex tori (<strong>Section 6.1</strong>); apply these methods to obtain irreducible examples of Kähler subgroups of direct products of surface groups which arise from maps onto higher-dimensional tori and use them to show that our conditions in Theorem 7.3.1 are minimal (<strong>Theorem A</strong>); apply our construction methods to produce irreducible examples of Kähler groups that (i) have a classifying space with finite (n-1)-skeleton but no classifying space with finite n-skeleton and (ii) do not have a subgroup of finite index which embeds in a direct product of surface groups (<strong>Theorem 8.3.1</strong>); provide a new proof of Biswas, Mj and Pancholi's generalisation of Dimca, Papadima and Suciu's construction to more general maps onto elliptic curves (<strong>Theorem 4.3.2</strong>) and introduce invariants that distinguish many of the groups obtained from this construction (<strong>Theorem 4.6.2</strong>); and, construct explicit finite presentations for Dimca, Papadima and Suciu's groups thereby answering Question 3 (<strong>Theorem 5.4.4)</strong>).

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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 implemented in the computational algebra system MAGMA and employs Aschbacher's theorem to break the problem into several cases. The attached CD contains the code for the algorithm as well as several test cases which demonstrate the improvement over MAGMA's existing algorithm.

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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 investigates an algorithm to induce representations of large finite simple groups from a representation of a subgroup.

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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 commutante" des systemes nous permet de decrire, par le biais des groupes pointes, la restriction des systemes de auslander-reiten au vortex de leur terme extreme, et de donner un critere pour que ce vortex coincide avec celui du systeme. En particulier on a egalite pour les suites presque scindees se terminant par un module simple

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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, and we specify this list and provide exact values for P[subscript(G,Soc(G))](2) in these cases. We conclude Part I by showing that for all almost simple groups P[subscript(G,Soc(G))](3)≥139/150. In Part II we consider a related notion. Given a probability ε, we wish to determine d[superscript(ε)] (G), the number of random elements needed to generate a finite group G with failure probabilty at most ε. A generalisation of a result of Lubotzky bounds d[superscript(ε)](G) in terms of l(G), the chief length of G, and d(G), the minimal number of generators needed to generate G. We obtain bounds on the chief length of permutation groups in terms of the degree n, and bounds on the chief length of completely reducible matrix groups in terms of the dimension and field size. Combining these with existing bounds on d(G), we obtain bounds on d[superscript(ε)] (G) for permutation groups and completely reducible matrix groups.

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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 P'∩Z(P). A long standing conjecture of Charles C. Sims states that the number of groups of order p<sup>m</sup> is<br/> p<sup><sup>2</sup>andfrasl;<sub>27</sub>m<sup>3</sup>+O(m<sup>2</sup>)</sup>. (1) We show that the number of groups of nilpotency class at most 3 and order p<sup>m</sup> satisfies (1). We prove a similar result concerning the number of graded Lie rings of order p<sup>m</sup> generated by their first grading.

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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 tree class of components of these modules induced up to G.

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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 fini de groupes librement indécomposables en termes de présentation des facteurs et de leurs groupes d'automorphismes a été donnée par Fouxe-Rabinovich. Il découle de son travail que si les facteurs et leurs groupes d'automorphismes sont de présentation finie, alors le groupe d'automorphisme du produit libre est de présentation finie. Une première partie de cette thèse donne une nouvelle preuve de ce résultat, se basant sur le langage des actions de groupes sur les arbres.<p><p>Un groupe accessible est un groupe de type fini déterminé par un graphe de groupe fini dont les groupes d'arêtes sont finis et les groupes de sommets ont au plus un bout, c'est-à-dire qu'ils ne se décomposent pas en produit amalgamé ni en extension HNN sur un groupe fini. L'étude du groupe d'automorphisme d'un groupe accessible est ramenée à l'étude de groupes d'automorphismes de produits libres, de groupes de twists de Dehn et de groupes d'automorphismes relatifs des groupes de sommets. En particulier, on déduit un critère naturel pour que le groupe d'automorphismes d'un groupe accessible soit de présentation finie, et on donne une caractérisation des groupes accessibles dont le groupe d'automorphisme externe est fini. Appliqués aux groupes hyperboliques de Gromov, ces résultats permettent d'affirmer que le groupe d'automorphismes d'un groupe hyperbolique est de présentation finie, et donnent une caractérisation précise des groupes hyperboliques dont le groupe d'automorphisme externe est fini.<p><p>Enfin, on étudie le rang des groupes de Coxeter, c'est-à-dire le cardinal minimal d'un ensemble générateur pour un groupe de Coxeter donné. Plus précisément, on montre que si les composantes de la matrice de Coxeter déterminant un groupe de Coxeter sont suffisamment grandes, alors l'ensemble générateur standard est de cardinal minimal parmi tous les ensembles générateurs.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished

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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 dans unquotient fini de Nous avons prouve que 7Ti(5) est omnipotent quand S estune surface autre que P2, T2 ou K2. Cela generalise le fait, deja connu, que lesgroupes libres sont omnipotents. La preuve utilise principalement des techniquesgeometriques impliquant des graphiques d'espaces ayant pour but de retractercertains espaces en graphiques.

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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 \(Gal(\bar{K}/K)\), and we find a host of new categories which answer the Question of Ihara/Conjecture of Oda-Matsumura.<br>Mathematics

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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 application of DFT are generalized Scherk-Schwarz compactifications. They give rise to half-maximal, electrically gauged supergravities which are classified by the embedding tensor formalism, specifying the embedding of their gauge group into O(n,n). Because it is not compatible with all solutions of the embedding tensor, the strong constraint is replaced by the closure constraint of DFT's flux formulation. This allows for compactifications on backgrounds which are not T-dual to well-defined geometric ones. Their description requires non-geometric fluxes. Due to their special properties, they are also of particular phenomenological interest. However, the violation of the strong constraint obscures their uplift to full string theory. Moreover, there is an ambiguity in generalizing traditional Scherk-Schwarz compactifications to the doubled space of DFT: There is a lack of a general procedure to construct the twist of the compactification. After reviewing DFT and generalized Scherk-Schwarz compactifications, DFT_WZW, a generalization of the current formalism is presented. It captures the low energy dynamics of a closed bosonic string propagating on a compact group manifold and it allows to solve the problems mentioned above. Its classical action and the corresponding gauge transformations arise from Closed String Field Theory up to cubic order in the massless fields. These results are rewritten in terms of a generalized metric and extended to all orders in the fields. There is an explicit distinction between background and fluctuations. For the gauge algebra to close, the latter have to fulfill a modified strong constraint, while for the former the closure constraint is sufficient. Besides the generalized diffeomorphism invariance known from the traditional formulation, DFT_WZW is invariant under standard diffeomorphisms of the doubled space. They are broken by imposing the totally optional extended strong constraint. In doing so, the traditional formulation is restored. A flux formulation for the new theory is derived and its connection to generalized Scherk-Schwarz compactifications is discussed. Further, a possible tree-level uplift of a genuinely non-geometric background (not T-dual to any geometric configuration) is presented. Finally, the ambiguity in constructing the compactification's twist is eliminated. Altogether, a more general picture of DFT and the structures it is based on emerges.

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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 calculate the probability of generating a proper subgroup, other than the alternating group, by two elements one of which is an n-cyc1e and the other is chosen randomly. In Chapters 8 and 9 we give some of the programs written in GAP language, which used in the earlier work and which can be used by other workers in this area.

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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 commuting probability Pr(G), i.e., the proportion of pairs of elements x,y Ε G which commute. What are the possible values of Pr(G)? What is the set of all possible values like as a subset of [0,1]? 3. What is the probability that a random permutation π Ε Sn has a fixed set of some predetermined size k? Particularly, how does this probability change as k grows? We give satisfactory answers to each of these questions, using a range of methods. More detailed abstracts are included at the beginning of each chapter.

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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 set for the free crossed module A2 δ2 AI, where δ2 is crossed module homo- morphism. Proposition 4.1 together with this free crossed module δ2 : A2  Al define a 2-dimensional free crossed resolution for A2 δ2 Al ɛG (see Proposition 4.9). We then define an exact sequence A3 δ2 A2 δ2A1, where A3, is an (Ai/ δ2A2)-module on generating set Z3 with module homomorphism δ3 : A3  A2 defined on the generators. Proposition 4.11 says that we have a crossed complex of length 3,i.e., A3 δ3 A2 δ2 Ai ε G, where Imδ3 C__ Kerδ2.

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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 mechanism which rewards agents according to a general-logit specification based on their relative ability. I derive conditions under which a team's performance is most sensitive to the ability of its highest-skill members, while at the same time higher spread in the distribution of ability has a positive effect on group output. In the final chapter I shift attention to the problem of optimal player order choice in dynamic pairwise team battles. I show that even if player order choice is conducted endogenously and sequentially after observing the outcomes of earlier rounds, then complete randomization over remaining agents is always a subgame perfect equilibrium. The zero-sum nature of these type of contests implies that expected payoffs for each team are independent of whether the contest matching pairs are determined endogenously and sequentially or announced before the start of the game. In both cases the ex-ante payoffs are equivalent to those when an independent contest organizer randomly draws the matches<br>Thesis (PhD) — Boston College, 2020<br>Submitted to: Boston College. Graduate School of Arts and Sciences<br>Discipline: Economics

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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, and to compute its corrections. Then, we try to build a bridge between the sound results of RMT and Renormalisation Group methods in order to investigate the spectral properties of the Scale Free and Small World class of networks. In particular, we propose a mechanism who could help understanding the behaviour of self similar network structures with low diameter.

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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<sub>K</sub> and do not embed w*<sub>1</sub>. Each interval in N or R embeds every ordinal of cardinality N<sub>K</sub> and every countable converse ordinal. N and R then embed every K-type of cardinality N<sub>K</sub> with no uncountable descending chains. Hence any such order type can be written as a countable union of wellordered types, each of order type smaller than w<sup>w</sup><sub>k</sub>. In particular, if α is an ordinal between w<sup>w</sup><sub>k</sub> and w<sub>K+1</sub>, and A is a set of order type α then A= ⋃<sub>n<w</sub>A<sub>n</sub> where each A<sub>n</sub> has order type w<sup>n</sup><sub>k</sub>. If X is a subset of N with X and N - X dense in N, then X is orderisomorphic to R, whence any dense subset of R has the same order type as R. If Y is any subset of R then R is (finitely) piece- wise order-preserving isomorphic (PWOP) to R ⋃<sup>.</sup> Y. Thus there is only one PWOP equivalence class of N<sub>K</sub>-dense K-types which have cardinality N<sub>K</sub>, and which do not embed w*<sub>1</sub>. There are N<sub>K+1</sub> PWOP equivalence classes of ordinals of cardinality N</sub>K</sub>. Hence the PWOP automorphisms of R have N<sub>K+1</sub> orbits on θ(R). The countably piece- wise orderpreserving automorphisms of R have N<sub>0</sub> orbits on R if ∣k∣ is smaller than w<sub>1</sub> and ∣k∣ if it is not smaller.

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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 Chapter 3, the properties of multilinear functions are investigated and the theory is developed to make them useful for formulating the representation of groups. It will be found that multilinear functions are more flexible than their tensor or matrix counterparts in traditional linear algebra. Multilinear functions can be classified according to the symmetry class of their arguments and their behaviour under the monogenic or harmonic decomposition. It is found that the previous definitions of monogenic and harmonic functions need some modification if they are to be defined consistently. Polynomial projection is also discussed, a technique that is useful in constructing non-linear functions from linear functions, an operation outside the scope of conventional linear algebra. In Chapter 4, multilinear functions are used to construct the irreducible representations of the three regular classes of classical groups; rotation groups, the special unitary and special linear group, and the symplectic group. In each case it is found that a decomposition must be applied to the multilinear functions in order to find the irreducible representations of the groups. For the representations of some of the groups this entails finding the harmonic or monogenic parts of the functions. The groups can be realised as subgroups of the spin group of some dimension and signature. However, geometric algebra provides such a rich algebraic structure that the representations of the groups can be realised in more than one way. In Chapter 7 a brief review is given of computer software for performing symbolic calculations with geometric algebra. A new software package which performs semi-symbolic manipulation of multivectors in spaces of any dimension and signature is presented.

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