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Dissertations / Theses on the topic 'Group theory – Mathematics'

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Published: 4 June 2021
Last updated: 16 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

Gatward, Sally Morrell. "On a new construction in group theory." Thesis, Queen Mary, University of London, 2011. http://qmro.qmul.ac.uk/xmlui/handle/123456789/2342.

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My supervisors Ian Chiswell and Thomas M¨uller have found a new class of groups of functions defined on intervals of the real line, with multiplication defined by analogy with multiplication in free groups. I have extended this idea to functions defined on a densely ordered abelian group. This doesn’t give rise to a class of groups straight away, but using the idea of exponentiation from a paper by Myasnikov, Remeslennikov and Serbin, I have formed another class of groups, in which each group contains a subgroup isomorphic to one of Chiswell and M¨uller’s groups. After the introduction, the se
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8

Nicholson, Julia. "Otto Hölder 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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9

Hert, Theresa Marie. "An efficient presentation of PGL(2,p)." CSUSB ScholarWorks, 1993. https://scholarworks.lib.csusb.edu/etd-project/690.

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10

Bavuma, Yanga. "Some combinatorial aspects in algebraic topology and geometric group theory." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29763.

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The present Msc thesis deals with classical topics of topology and it has been written, referring to [C. Kosniowski, Introduction to Algebraic Topology, Cambridge University Press, 1980, Cambridge], which is a well known textbook of algebraic topology. It has been selected a list of main exercises from this reference, whose solutions were not directly available, or subject to differerent methods. In fact combinatorial methods have been preferred and the result is a self-contained dissertation on the theory of the fundamental group and of the coverings. Finally, there are some recent problems i
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11

Yeo, Michelle SoYeong. "CONSTRUCTION OF FINITE GROUP." CSUSB ScholarWorks, 2017. https://scholarworks.lib.csusb.edu/etd/592.

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The main goal of this project is to present my investigation of finite images of the progenitor 2^(*n) : N for various N and several values of n. We construct each image by using the technique of double coset enumeration and give a proof of the isomorphism type of the image. We obtain the group 7^2: D_6 as a homomorphic image of the progenitor 2^(*14) : D_14, we obtain the group 2^4 : (5 : 4) as a homomorphic image of the progenitor 2^(*5) : (5 : 4), we obtain the group (10 x10) : ((3 x 4) : 2) as a homomorphic image of the progenitor 2^(*15) : (15x4), we obtain the group PGL(2; 7) as a homomo
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12

Kilgour, Calum Wallace. "Using pictures in combinatorial group and semigroup theory." Thesis, University of Glasgow, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265965.

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13

Fennessey, Eric James. "Some applications of geometric techniques in combinatorial group theory." Thesis, University of Glasgow, 1989. http://theses.gla.ac.uk/6159/.

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Combinatorial group theory abounds with geometrical techniques. In this thesis we apply some of them to three distinct areas. In Chapter 1 we present all of the techniques and background material neccessary to read chapters 2,3,4. We begin by defining complexes with involutary edges and define coverings of these. We then discuss equivalences between complexes and use these in §§1.3 and 1.4 to give a way (the level method) of simplifying complexes and an application of this method (Theorem 1.3). We then discuss star-complexes of complexes. Next we present background material on diagrams and pic
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14

Wharton, Elizabeth. "The model theory of certain infinite soluble groups." Thesis, University of Oxford, 2006. http://ora.ox.ac.uk/objects/uuid:7bd8d05b-4ff6-4326-8463-f896e2862e25.

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This thesis is concerned with aspects of the model theory of infinite soluble groups. The results proved lie on the border between group theory and model theory: the questions asked are of a model-theoretic nature but the techniques used are mainly group-theoretic in character. We present a characterization of those groups contained in the universal closure of a restricted wreath product U wr G, where U is an abelian group of zero or finite square-free exponent and G is a torsion-free soluble group with a bound on the class of its nilpotent subgroups. For certain choices of G we are able to us
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15

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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16

Vaintrob, Dmitry. "Mirror symmetry and the K theory of a p-adic group." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104578.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 59-61).<br>Let G be a split, semisimple p-adic group. We construct a derived localization functor Loc : ... from the compactified category of [BK2] associated to G to the category of equivariant sheaves on the Bruhat-Tits building whose stalks have finite-multiplicity isotypic components as representations of the stabilizer. Our construction is motivated by the "coherent-constructible correspondence" functor in toric mirr
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17

Ketcham, Kwang B. "Group Frames and Partially Ranked Data." Scholarship @ Claremont, 2010. https://scholarship.claremont.edu/hmc_theses/19.

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We give an overview of finite group frames and their applications to calculating summary statistics from partially ranked data, drawing upon the work of Rachel Cranfill (2009). We also provide a summary of the representation theory of compact Lie groups. We introduce both of these concepts as possible avenues beyond finite group representations, and also to suggest exploration into calculating summary statistics on Hilbert spaces using representations of Lie groups acting upon those spaces.
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18

Joubert, Paul. "Geometric actions of the absolute Galois group." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/2508.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2006.<br>This thesis gives an introduction to some of the ideas originating from A. Grothendieck's 1984 manuscript Esquisse d'un programme. Most of these ideas are related to a new geometric approach to studying the absolute Galois group over the rationals by considering its action on certain geometric objects such as dessins d'enfants (called stick figures in this thesis) and the fundamental groups of certain moduli spaces of curves. I start by defining stick figures and explaining the connection between these innocent combinatoria
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19

Pearce, Geoffrey. "Transitive decompositions of graphs." University of Western Australia. School of Mathematics and Statistics, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0087.

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A transitive decomposition of a graph is a partition of the arc set such that there exists a group of automorphisms of the graph which preserves and acts transitively on the partition. This turns out to be a very broad idea, with several striking connections with other areas of mathematics. In this thesis we first develop some general theory of transitive decompositions, and in particular we illustrate some of the more interesting connections with certain combinatorial and geometric structures. We then give complete, or nearly complete, structural characterisations of certain classes of transi
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20

Adovasio, Ben. "A Character Theory Free Proof of Burnside's paqb Theorem." Youngstown State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1337975956.

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21

Melhuish, Kathleen Mary. "The Design and Validation of a Group Theory Concept Inventory." PDXScholar, 2015. https://pdxscholar.library.pdx.edu/open_access_etds/2490.

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Within undergraduate mathematics education, there are few validated instruments designed for large-scale usage. The Group Concept Inventory (GCI) was created as an instrument to evaluate student conceptions related to introductory group theory topics. The inventory was created in three phases: domain analysis, question creation, and field-testing. The domain analysis phase included using an expert consensus protocol to arrive at the topics to be assessed, analyzing curriculum, and reviewing literature. From this analysis, items were created, evaluated, and field-tested. First, 383 students ans
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22

George, Timothy Edward. "Symmetric representation of elements of finite groups." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3105.

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The purpose of the thesis is to give an alternative and more efficient method for working with finite groups by constructing finite groups as homomorphic images of progenitors. The method introduced can be applied to all finite groups that possess symmetric generating sets of involutions. Such groups include all finite non-abelian simple groups, which can then be constructed by the technique of manual double coset enumeration.
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23

Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.

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The conjugacy length function of a group Γ determines, for a given a pair of conjugate elements u,v ∈ Γ, an upper bound for the shortest γ in Γ such that uγ = γv, relative to the lengths of u and v. This thesis focuses on estimating the conjugacy length function in certain finitely generated groups. We first look at a collection of solvable groups. We see how the lamplighter groups have a linear conjugacy length function; we find a cubic upper bound for free solvable groups; for solvable Baumslag--Solitar groups it is linear, while for a larger family of abelian-by-cyclic groups we get either
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24

Hicks, Katrina. "The representation theory of some groups with blocks of defect group C←3 times C←3 in characteristic three." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239319.

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25

Montanaro, William M. Jr. "Character Degree Graphs of Almost Simple Groups." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1398345504.

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26

Woodruff, Benjamin M. "Statistical Properties of Thompson's Group and Random Pseudo Manifolds." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd854.pdf.

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27

Oberholzer, Ria M. "On subnormal subgroups in factorized groups." Thesis, Stellenbosch : Stellenbosch University, 2004. http://hdl.handle.net/10019.1/50050.

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Thesis (MSc) -- Stellenbosch University, 2004.<br>ENGLISH ABSTRACT: In this thesis we give a survey of research done on a problem on subnormal subgroups in factorized groups G = AB, where A and B are two subgroups of G with H a subgroup of A n B which is subnormal in both A and B. It is of interest to know whether or not such a subgroup H will also be subnormal in G. During the past twenty five to thirty years some positive results were obtained in the case where G is a finite group. This was mainly due to work done by Maier and Wielandt, with results by Sidki and Casolo following shortl
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28

Aivazidis, Stefanos. "On the subgroup permutability degree of some finite simple groups." Thesis, Queen Mary, University of London, 2015. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8899.

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Consider a finite group G and subgroups H;K of G. We say that H and K permute if HK = KH and call H a permutable subgroup if H permutes with every subgroup of G. A group G is called quasi-Dedekind if all subgroups of G are permutable. We can define, for every finite group G, an arithmetic quantity that measures the probability that two subgroups (chosen uniformly at random with replacement) permute and we call this measure the subgroup permutability degree of G. This measure quantifies, among others, how close a finite group is to being quasi-Dedekind, or, equivalently, nilpotent with modular
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29

Summers, Andrew. "The Influence of Subgroup Structure on Finite Groups Which are the Product of Two Subgroups." Youngstown State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1620058166407179.

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30

Maurer, Kendall Nicole. "Minimally Simple Groups and Burnside's Theorem." University of Akron / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1271041194.

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31

Davidson, Peter John. "Geometric methods in the study of Pride groups and relative presentations." Thesis, Connect to e-thesis, 2008. http://theses.gla.ac.uk/230/.

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Thesis (Ph.D.) - University of Glasgow, 2008.<br>Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, Department of Mathematics, University of Glasgow, 2008. Includes bibliographical references. Print version also available.
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32

Puente, Philip C. "Crystallographic Complex Reflection Groups and the Braid Conjecture." Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011877/.

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Crystallographic complex reflection groups are generated by reflections about affine hyperplanes in complex space and stabilize a full rank lattice. These analogs of affine Weyl groups have infinite order and were classified by V.L. Popov in 1982. The classical Braid theorem (first established by E. Artin and E. Brieskorn) asserts that the Artin group of a reflection group (finite or affine Weyl) gives the fundamental group of regular orbits. In other words, the fundamental group of the space with reflecting hyperplanes removed has a presentation mimicking that of the Coxeter presentation;
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33

MacKinnon, Benjamin B. "The Automorphism Group of the Halved Cube." VCU Scholars Compass, 2016. http://scholarscompass.vcu.edu/etd/4609.

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An n-dimensional halved cube is a graph whose vertices are the binary strings of length n, where two vertices are adjacent if and only if they differ in exactly two positions. It can be regarded as the graph whose vertex set is one partite set of the n-dimensional hypercube, with an edge joining vertices at hamming distance two. In this thesis we compute the automorphism groups of the halved cubes by embedding them in R n and realizing the automorphism group as a subgroup of GLn(R). As an application we show that a halved cube is a circulant graph if and only if its dimension of is at most fou
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34

Iverson, Nate. "A Phan-like theorem for orthogonal groups in even characteristic." Bowling Green State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1280251081.

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35

McHugh, John. "Monomial Characters of Finite Groups." ScholarWorks @ UVM, 2016. http://scholarworks.uvm.edu/graddis/572.

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An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters – those induced from a linear character of some subgroup – since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the class of M-groups, those groups all of whose irreducible characters are monomial. A classical theorem of Taketa asserts that an M-group is necessarily solvable, and Dade proved that every solvable group ca
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36

Bergeron, Maxime. "On CAT(0) aspects of geometric group theory and some applications to geometric superrigidity." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=110571.

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Since their popularization by Gromov in the eighties, CAT(0) metric spaces of bounded curvature as defined by Alexandrov have been the locus of great progress in infinite group theory. Surveying ideas and constructions of geometric group theory, we express a bias towards groups acting on structures of this kind. As such, swiftly acquainting the reader with the theory of CAT(0) spaces, we provide a variety of examples obtained by gluing together families of convex polyhedra along their isometric faces. In this context, Gromov's link condition provides a local-to-global framework for non-positiv
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37

Hamilton, Martin. "Finiteness conditions in group cohomology." Thesis, Connect to e-thesis, 2008. http://theses.gla.ac.uk/182/.

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Thesis (Ph.D.) - University of Glasgow, 2008.<br>Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, University of Glasgow, 2008. Includes bibliographical references. Print version also available.
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38

Housley, Matthew L. "Conjugacy Classes of the Piecewise Linear Group." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1442.pdf.

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39

Ioannou, M. "Conceptual and learning issues in mathematics undergraduates' first encounter with group theory : a commognitive analysis." Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/39453/.

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40

Bounds, Jordan. "On the quasi-isometric rigidity of a class of right-angled Coxeter groups." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1561561078356503.

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41

Holik, Nicklos L. III. "NONSTANDARD HULLS OF GROUPS." University of Akron / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1176409770.

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42

Aafif, Amal Boyer Robert Paul Krandick Werner J. "Non-commutative harmonic analysis on certain semi-direct product groups /." Philadelphia, Pa. : Drexel University, 2007. http://hdl.handle.net/1860/1767.

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43

Song, Sung Yell. "The character tables of certain association schemes /." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487329662147808.

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44

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
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45

Aubad, Ali. "On commuting involution graphs of certain finite groups." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/on-commuting-involution-graphs-of-certain-finite-groups(009c80f5-b0d6-4164-aefc-f783f74c80f1).html.

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46

Pant, Sujan. "Structural results in group von Neumann algebra." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5822.

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Chifan, Kida, and myself introduced a new class of non-amenable groups denoted by ${\bf NC} \cap {\bf Quot}(\mathcal C_{rss})$ which gives rise to \emph{prime} von Neumann algebras. This means that for every $\G\in {\bf NC} \cap {\bf Quot}(\mathcal C_{rss})$ its group von Neumann algebra $L(\G)$ cannot be decomposed as a tensor product of diffuse von Neumann algebras. The class ${\bf NC} \cap {\bf Quot}(\mathcal C_{rss})$ is fairly large as it contains many natural examples of groups, some intensively studied in various areas of mathematics: all infinite central quotients of pure surface braid
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47

Kreighbaum, Kevin M. "Combinatorial Problems Related to the Representation Theory of the Symmetric Group." University of Akron / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=akron1270830566.

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48

Klein, Tom. "Filtered ends of pairs of groups." Diss., Online access via UMI:, 2007.

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49

Wheeler, Jessica. "Instructing Group Theory Concepts from Pre-Kindergarten to College through Movement Activities." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461184131.

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50

Weighill, Thomas. "Bifibrational duality in non-abelian algebra and the theory of databases." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/96125.

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Thesis (MSc)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: In this thesis we develop a self-dual categorical approach to some topics in non-abelian algebra, which is based on replacing the framework of a category with that of a category equipped with a functor to it. We also make some first steps towards a possible link between this theory and the theory of databases in computer science. Both of these theories are based around the study of Grothendieck bifibrations and their generalisations. The main results in this thesis concern correspondences between certain structures on a ca
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