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Dissertations / Theses on the topic 'Polycyclic groups][Algebraic groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Du, Sautoy M. P. F. "Discrete groups, analytic groups and Poincare series." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236109.

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2

Assmann, Björn. "Applications of Lie methods to computations with polycyclic groups." Thesis, St Andrews, 2007. http://hdl.handle.net/10023/435.

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3

Silva, Jefferson dos Santos e. "Uma apresentação policíclica para o multiplicador de Schur e o quadrado tensorial não abeliano de um grupo policíclico." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4539.

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Submitted by Erika Demachki (erikademachki@gmail.com) on 2015-05-18T18:27:17Z No. of bitstreams: 2 Dissertação - Jefferson dos Santos e Silva - 2015.pdf: 741852 bytes, checksum: 8cb431ec9a186100784d60268a133fcf (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2015-05-18T18:28:34Z (GMT) No. of bitstreams: 2 Dissertação - Jefferson dos Santos e Silva - 2015.pdf: 741852 bytes, checksum: 8cb431ec9a186100784d60268a133fcf (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a77147

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4

Garibaldi, Skip. "Trialitarian algebraic groups /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1998. http://wwwlib.umi.com/cr/ucsd/fullcit?p9906492.

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5

Meyer, Aurel Nathan. "Essential dimension of algebraic groups." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/27091.

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We study the essential dimension of linear algebraic groups. For a group G, essential dimension is a measure for the complexity of G-torsors or, more generally, the complexity of any algebraic or geometric structure with automorphism group G. This makes essential dimension a powerful invariant with many interesting and surprising connections to problems in algebra and geometry. We show that for various classes of groups, including finite (algebraic) groups and algebraic tori, the essential dimension is related to minimal faithful representations. In many cases this renders the exact value of t

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6

Brundan, Jonathan Walter. "Double cosets in algebraic groups." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244137.

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7

Craven, David Andrew. "Algebraic modules for finite groups." Thesis, University of Oxford, 2007. http://ora.ox.ac.uk/objects/uuid:7f641b33-d301-4445-8269-a5a33f4b7e5e.

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The main focus of this thesis is algebraic modules---modules that satisfy a polynomial equation with integer co-efficients in the Green ring---in various finite groups, as well as their general theory. In particular, we ask the question `when are all the simple modules for a finite group G algebraic?' We call this the (p-)SMA property. The first chapter introduces the topic and deals with preliminary results, together with the trivial first results. The second chapter provides the general theory of algebraic modules, with particular attention to the relationship between algebraic modules and t

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8

Clarke, Matthew Charles. "Unipotent elements in algebraic groups." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/241660.

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This thesis is concerned with three distinct, but closely related, research topics focusing on the unipotent elements of a connected reductive algebraic group G, over an algebraically closed field k, and nilpotent elements in the Lie algebra g = LieG. The first topic is a determination of canonical forms for unipotent classes and nilpotent orbits of G. Using an original approach, we begin by obtaining a new canonical form for nilpotent matrices, up to similarity, which is symmetric with respect to the non-main diagonal (i.e. it is fixed by the map f : (xi;j) -> (xn+1-j;n+1-i)), with entries in

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9

Dos, Santos João Pedro Pinto. "Fundamental groups in algebraic geometry." Thesis, University of Cambridge, 2006. https://www.repository.cam.ac.uk/handle/1810/252015.

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10

Sinanan, Shavak. "Algorithms for polycyclic-by-finite groups." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/49186/.

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A set of fundamental algorithms for computing with polycyclic-by-finite groups is presented here. Polycyclic-by-finite groups arise naturally in a number of contexts; for example, as automorphism groups of large finite soluble groups, as quotients of finitely presented groups, and as extensions of modules by groups. No existing mode of representation is suitable for these groups, since they will typically not have a convenient faithful permutation representation. A mixed mode is used to represent elements of such a group; utilising a polycyclic presentation or a power-conjugate presentation fo

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11

Stalder, Nicolas Raymond. "Algebraic monodromy groups of A-motives /." Zürich : ETH, 2007. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=17369.

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12

Proud, Richard. "Unipotent subgroups of reductive algebraic groups." Thesis, University of Warwick, 1997. http://wrap.warwick.ac.uk/57023/.

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Let G be a connected reductive algebraic group defined over an algebraically closed field of good characteristic p>0. Suppose uEG has order p. In [T2] it is shown that u lies in a closed reductive subgroup of G of type Al. This is the best possible group theoretic analogue of the Jacobson-Morozov theorem for simple Lie algebras. Testerman's key result is a type of `exponentiation process'. For our given element u, this process constructs a 1-dimensional connected abelian unipotent subgroup of G, hence isomorphic to Ga, containing u. This in turn yields the required Al overgroup of u. Now let 1

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13

Rainone, Raffaele. "Geometric actions of classical algebraic groups." Thesis, University of Southampton, 2014. https://eprints.soton.ac.uk/366485/.

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Let k be an algebraically closed field of arbitrary characteristic p. An affine algebraic group G is an affine algebraic variety over k with a group structure such that multiplication and inversion maps are morphisms of varieties. A special class of affine algebraic groups are the so called classical groups Cl(V), groups of isometries of a finite dimensional k-vector space V with respect to a certain form on V {e.g. a zero form, a symplectic form or a non-degenerate quadratic form. These groups are: GL(V) the general linear group, Sp(V) the symplectic group and O(V) the orthogonal group. Let G

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14

Wright, William G. (William Glenn). "An algebraic characterization of stability groups." Thesis, University of North Texas, 1991. https://digital.library.unt.edu/ark:/67531/metadc332465/.

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The goal of this paper is to establish necessary and sufficient conditions for a subgroup of the full homeomorphism group of a manifold to be the stability group of a point in the underlying space. Such subgroups are useful in identifying the underlying space in terms of its homeomorphism group even in cases in which this space is not necessarily a manifold. Thus, stability groups are useful in classifying various spaces.

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15

Anwar, Muhammad F. "Representations and cohomology of algebraic groups." Thesis, University of York, 2011. http://etheses.whiterose.ac.uk/2032/.

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Let G be a semisimple simply connected linear algebraic group over an algebraically closed field k of characteristic p. In [11], Donkin gave a recursive description for the characters of cohomology of line bundles on the flag variety G/B with G = SL3. In chapter 2 of this thesis we try to give a non recursive description for these characters. In chapter 3, we give the first step of a version of formulae in [11] for G = G2. In his famous paper [7], Demazure introduced certain indecomposable modules and used them to give a short proof of the Borel-Weil-Bott theorem (characteristic zero). In chap

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16

Thomas, Adam Robert. "Irreducible subgroups of exceptional algebraic groups." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/28689.

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Let $G$ be a semisimple algebraic group over an algebraically closed field $K$, of characteristic $p \geq 0$. A closed subgroup of $G$ is said to be irreducible if it does not lie in any proper parabolic subgroup of $G$. In this thesis we address the following problem: classify the connected irreducible subgroups of $G$, up to conjugacy, where $G$ is of exceptional type. Work of Liebeck and Seitz classifies the conjugacy classes of simple, connected irreducible subgroups of rank at least 2, with a restriction on the characteristic of the underlying field ($p > 7$ is sufficient). When $G$ is of

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17

Penrod, Keith. "Infinite product groups /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1977.pdf.

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18

Cook, Martin David. "Conjugacy class structure in simple algebraic groups." Thesis, Lancaster University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442727.

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19

Litterick, Alastair. "Finite simple subgroups of exceptional algebraic groups." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/14278.

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Let G = G(K) be a simple algebraic group over an algebraically closed field K of characteristic p ≥ 0. The study of subgroups of G splits naturally according to whether G is of classical or exceptional type, and according to whether the subgroups considered are finite or of positive dimension. This thesis considers finite subgroups of adjoint groups G of exceptional type. A finite subgroup of G is called Lie primitive if it lies in no proper, closed subgroup of positive dimension. This is a natural maximality condition and, when studying Lie primitive subgroups, a reduction theorem due to Bo

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20

Rizkallah, John. "Bounding cohomology for low rank algebraic groups." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/267214.

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Let G be a semisimple linear algebraic group over an algebraically closed field of prime characteristic. In this thesis we outline the theory of such groups and their cohomology. We then concentrate on algebraic groups in rank 1 and 2, and prove some new results in their bounding cohomology.

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21

Vallino, Daniele. "Algebraic and definable closure in free groups." Thesis, Lyon 1, 2012. http://www.theses.fr/2012LYO10090/document.

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Nous étudions la clôture algébrique et définissable dans les groupes libres. Les résultats principaux peuvent être résumés comme suit. Nous montrons un résultat de constructibilité des groupes hyperboliques sans torsion au-dessus de la clôture algébrique d'un sous-ensemble engendrant un groupe non abélien. Nous avons cherché à comprendre la place qu'occupe la clôture algébrique acl_G(A) dans certaines décompositions de G. Nous avons étudié la possibilité de la généralisation de la méthode de Bestvina-Paulin dans d'autres directions, en considérant les groupes de type fini qui agissent d'une ma

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22

Iannone, Paola. "Automorphism groups of geometric codes." Thesis, University of East Anglia, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318091.

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23

Henes, Matthew Thomas. "Root subgroups of the rank two unitary groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2841.

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Discusses certain one-parameter subgroups of the low-rank unitary groups called root subgroups. Unitary groups also have representations of Lie type which means they consist of transformations that act as automorphisms of an underlying Lie algebra, in this case the special linear algebra. Exploring this definition of the unitary groups, we find a correlation, via exponentiation, to the basis elements of Lie algebra.

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24

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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25

Mohrdieck, Stephan. "Conjugacy classes of non-connected semisimple algebraic groups." [S.l. : s.n.], 2000. http://www.sub.uni-hamburg.de/disse/172/diss.pdf.

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26

Turner, S. M. "Hasse-Weil zeta functions for linear algebraic groups." Thesis, University of Glasgow, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318888.

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27

Costantini, Mauro. "On the lattice automorphisms of certain algebraic groups." Thesis, University of Warwick, 1989. http://wrap.warwick.ac.uk/101705/.

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In the first chapter we give an introduction, and a survey of known results, which we shall use throughout the dissertation. In the second chapter we first prove that every projectivity of a connected reductive non-abelian algebraic group G over K = Fp is strictly index-preserving (Theorem 2.1.6.). Then we prove that every autoprojectivity of G induces an automorphism of the building canonically associated to O. Furthermore we show how certain autoprojectivities of G act on the Weyl group of G and on the Dynkin diagram of G. In the third chapter we restrict our attention to simple algebraic gr

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28

Hazi, Amit. "Semisimple filtrations of tilting modules for algebraic groups." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/271774.

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Let $G$ be a reductive algebraic group over an algebraically closed field $k$ of characteristic $p > 0$. The indecomposable tilting modules $\{T(\lambda)\}$ for $G$, which are labeled by highest weight, form an important class of self-dual representations over $k$. In this thesis we investigate semisimple filtrations of minimal length (Loewy series) of tilting modules. We first demonstrate a criterion for determining when tilting modules for arbitrary quasi-hereditary algebras are rigid, i.e. have a unique Loewy series. Our criterion involves checking that $T(\lambda)$ does not have certain su

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29

Stewart, David I. "G-complete reducibility and the exceptional algebraic groups." Thesis, Imperial College London, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.528310.

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30

Edwards, T. "Algebraic 2-complexes over certain infinite abelian groups." Thesis, University College London (University of London), 2006. http://discovery.ucl.ac.uk/1444701/.

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Whitehead's Theorem allows the study of homotopy types of two dimensional CW complexes to be phrased in terms of chain homotopy types of algebraic complexes, arising as the cellular chains on the universal cover. It is natural to ask whether the category of algebraic complexes fully represents the category of CW complexes, in particular whether every algebraic complex is realised geometrically. The case of two dimensional complexes is of special interest, partly due to the relationship between such complexes and group presentations and partly since, as was recently proved, it relates to the qu

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31

Deshpande, D. V. "Topological methods in algebraic geometry : cohomology rings, algebraic cobordism and higher Chow groups." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.598515.

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This thesis is divided into three chapters. The first chapter is about the cohomology ring of the space of rotational functions. In the second chapter, we define algebraic cobordism of classifying spaces, Ω*(<i>BG</i>) and <i>G</i>-equivariant algebraic cobordism Ω*<i><sub>G</sub></i>(-) for a linear algebraic group <i>G. </i>We prove some properties of the coniveau filtration on algebraic cobordism, denoted <i>F<sup>j</sup></i>(Ω*(-)); which are required for the definition to work. We show that <i>G</i>-equivariant cobordism satisfies the localization exact sequence. We compute Ω*(<i>BG</i>)

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32

Delgado, Rodríguez Jordi. "Extensions of free groups: algebraic, geometric, and algorithmic aspects." Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/458522.

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In this work we use geometric techniques in order to study certain natural extensions of free groups, and solve several algorithmic problems on them. To this end, we consider the family of free-abelian times free groups (Zm x Fn) as a seed towards further generalization in two main directions: semidirect products, and partially commuative groups (PC-groups). The four principal projects of this thesis are the following: Direct products of free-abelian and free groups We begin by studying the structure of the groups Zm x Fn , with special emphasis on their lattice of subgroups, and the

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33

Haller, Sergei. "Computing Galois cohomology and forms of linear algebraic groups." Giessen Giessener Elektronische Bibliothek, 2005. http://geb.uni-giessen.de/geb/volltexte/2005/2474/index.html.

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34

Shin, Hyunshik. "Algebraic degrees of stretch factors in mapping class groups." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51910.

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Given a closed surface Sg of genus g, a mapping class f in \MCG(Sg) is said to be pseudo-Anosov if it preserves a pair of transverse measured foliations such that one is expanding and the other one is contracting by a number \lambda(f). The number \lambda(f) is called a stretch factor (or dilatation) of f. Thurston showed that a stretch factor is an algebraic integer with degree bounded above by 6g-6. However, little is known about which degrees occur. Using train tracks on surfaces, we explicitly construct pseudo-Anosov maps on Sg with orientable foliations whose stretch factor \lambda has a

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35

Bowman, Christopher David. "Algebraic groups, diagram algebras, and their Schur-Weyl dualities." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610216.

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36

Humphreys, Jodie John Arthur Michael. "Algebraic properties of semi-simple lattices and related groups." Thesis, University College London (University of London), 2005. http://discovery.ucl.ac.uk/1445592/.

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Two abstract theories are developed. The first concerns isomorphism in variants with the same multiplicative properties as the Euler characteristic. It is used to show that the index of a subgroup in a semi-simple lattice is deter mined by its isomorphism type when that index is finite. This is also proved to be the case for subgroups of finite index in free products of finitely many semi-simple lattices as well as certain non-trivial extensions of Z by surface groups. In addition, a criterion for the failure of this property is given which applies to a large class of central extensions. The s

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37

Yam, Sheung-chi Phillip. "Algebraic methods on some problems in finance /." Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk/hkuto/record.jsp?B25018723.

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38

Crawley-Boevey, W. W. "Polycyclic-by-finite affine group schemes and infinite soluble groups." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372868.

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39

Borge, I. C. "A cohomological approach to the classification of $p$-groups." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246353.

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In this thesis we apply methods from homological algebra to the study of finite $p$-groups. Let $G$ be a finite $p$-group and let $\mathbb{F}_p$ be the field of $p$ elements. We consider the cohomology groups $\operatorname{H}^1(G,\mathbb{F}_p)$ and $\operatorname{H}^2(G,\mathbb{F}_p)$ and the Massey product structure on these cohomology groups, which we use to deduce properties about $G$. We tie the classical theory of Massey products in with a general method from deformation theory for constructing hulls of functors and see how far the strictly defined Massey products can take us in this set

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40

Bays, Martin. "Categoricity results for exponential maps of 1-dimensional algebraic groups." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.526931.

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41

Dowerk, Philip. "Algebraic and Topological Properties of Unitary Groups of II_1 Factors." Doctoral thesis, Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-165242.

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The thesis is concerned with group theoretical properties of unitary groups, mainly of II_1 factors. The author gives a new and elementary proof of an result on extreme amenability, defines the bounded normal generation property and invariant automatic continuity property and proves these for various unitary groups of functional analytic types.

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42

Misseldine, Andrew F. "Algebraic and Combinatorial Properties of Schur Rings over Cyclic Groups." BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/5259.

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In this dissertation, we explore the nature of Schur rings over finite cyclic groups, both algebraically and combinatorially. We provide a survey of many fundamental properties and constructions of Schur rings over arbitrary finite groups. After specializing to the case of cyclic groups, we provide an extensive treatment of the idempotents of Schur rings and a description for the complete set of primitive idempotents. We also use Galois theory to provide a classification theorem of Schur rings over cyclic groups similar to a theorem of Leung and Man and use this classification to provide a for

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43

Kenneally, Darren John. "On eigenvectors for semisimple elements in actions of algebraic groups." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/224782.

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Let G be a simple simply connected algebraic group defined over an algebraically closed field K and V an irreducible module defined over K on which G acts. Let E denote the set of vectors in V which are eigenvectors for some non-central semisimple element of G and some eigenvalue in K*. We prove, with a short list of possible exceptions, that the dimension of Ē is strictly less than the dimension of V provided dim V > dim G + 2 and that there is equality otherwise. In particular, by considering only the eigenvalue 1, it follows that the closure of the union of fixed point spaces of non-centra

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44

Uchiyama, Tomohiro. "Separability and complete reducibility of subgroups of the Weyl group of a simple algebraic group." Thesis, University of Canterbury. Mathematics and Statistics, 2012. http://hdl.handle.net/10092/7150.

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Let G be a reductive algebraic group defined over an algebraically closed field of characteristic p. A subgroup H of G is called G-complete reducible whenever H is contained in a parabolic subgroup P of G, it is contained in some Levi subgroup of P. In this thesis, we present a pair of reductive subgroups H and M of G of type E_7 such that H<M and H is G-completely reducible but not M-completely reducible.

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45

Friedrich, Nina. "Automorphism groups of quadratic modules and manifolds." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/276986.

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In this thesis we prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules and quadratic modules to be well-behaved in any sense: for example, the quadratic form may be singular. This extends results by van der Kallen and Mirzaii--van der Kallen respectively. Combining these results with the machinery introduced by Galatius--Randal-Williams to prove homological stability for moduli spaces of simply-connected manifolds

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46

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

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47

Fitzgerald, J. G. M. "Weyl modules for groups of type B2 and G2." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257653.

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In this thesis we determine the submodule structure of a number of Weyl modules for algebraic groups with root systems B2 and G2. We use the Jantzen sum formula to find the composition factors of Weyl modules and go on to use homomorphisms between Weyl modules, given by H.H. Andersen, and the comparison of two filtrations of tensor products of Weyl modules to establish submodule structure. A computer program in the Prolog language is given which calculates the Jantzen sum formula. In addition we find one 2-dimensional Ext group for simple modules for type G2 in characteristic greater than or e

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48

Massold, Heinrich. "Labile und relative Reduktionstheorie über Zahlkörpern." Bonn : Mathematisches Institut der Universität, 2003. http://catalog.hathitrust.org/api/volumes/oclc/54890700.html.

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49

Burness, Timothy Charles. "Fixed point spaces in actions of finite and algebraic simple groups." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.421905.

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50

Lond, Daniel. "On Reductive Subgroups of Algebraic Groups and a Question of Külshammer." Thesis, University of Canterbury. Mathematics and Statistics, 2013. http://hdl.handle.net/10092/8033.

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This Thesis is motivated by two problems, each concerning representations (homomorphisms) of groups into a connected reductive algebraic group G over an algebraically closed field k. The first problem is due to B. Külshammer and is to do with representations of finite groups in G: Let Γ be a finite group and suppose k has characteristic p. Let Γp be a Sylow p-subgroup of Γ and let ρ : Γp → G be a representation. Are there only finitely many conjugacy classes of representations ρ' : Γ → G whose restriction to Γp is conjugate to ρ? The second problem follows the work of M. Liebeck and G. Sei

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