Relevant bibliographies by topics / General theory for finite groups / Dissertations / Theses

To see the other types of publications on this topic, follow the link: General theory for finite groups.

Dissertations / Theses on the topic 'General theory for finite groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 dissertations / theses for your research on the topic 'General theory for finite groups.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.

Neman, Azadeh. "Propriétés combinatoires et modèle-théoriques des groupes." Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00679429.

Full text

Abstract:

Notre travail ici concerne certaines pistes pour des constructions nouveaux groupes, et en particulier de contre-exemples à la conjecture de Cherlin-Zilber. On parvient à trouver une réponse pour la stabilité de groupes CSA existentiellement clos. On exhibe un mot de groupe en deux variables qui a la propriété d'indépendance par rapport à la classe de groupes hyperboliques sans torsion. On en déduit que l'équation correspondante donne la propriété d'indépendance des groupes CSA existentiellement clos, ce qui en particulier implique leur instabilité. En outre, on prouve que les équations, et en particulier les ensembles définissables sans quantificateurs, définissent des ensembles stables dans les boules bornées des produits libres de groupes, en utilisant la version finie du théorème de Ramsey. Enfin, on introduit certains groupes construits comme tours particulières de produits libres et d'extensions HNN.

APA, Harvard, Vancouver, ISO, and other styles

Taylor, Paul Anthony. "Computational investigation into finite groups." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/computational-investigation-into-finite-groups(8fe69098-a2d0-4717-b8d3-c91785add68c).html.

Full text

Abstract:

We briefly discuss the algorithm given in [Bates, Bundy, Perkins, Rowley, J. Algebra, 316(2):849-868, 2007] for determining the distance between two vertices in a commuting involution graph of a symmetric group.We develop the algorithm in [Bates, Rowley, Arch. Math. (Basel), 85(6):485-489, 2005] for computing a subgroup of the normalizer of a 2-subgroup X in a finite group G, examining in particular the issue of when to terminate the randomized procedure. The resultant algorithm is capable of handling subgroups X of order up to 512 and is suitable, for example, for matrix groups of large degree (an example calculation is given using 112x112 matrices over GF(2)).We also determine the suborbits of conjugacy classes of involutions in several of the sporadic simple groups?namely Janko's group J4, the Fischer sporadic groups, and the Thompson and Harada-Norton groups. We use our results to determine the structure of some graphs related to this data.We include implementations of the algorithms discussed in the computer algebra package MAGMA, as well as representative elements for the involution suborbits.

APA, Harvard, Vancouver, ISO, and other styles

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.

Full text

Abstract:

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 the composition factors of a group, and between algebraic modules and the Heller operator and Auslander--Reiten quiver. The third chapter concerns itself with indecomposable modules for dihedral and elementary abelian groups. The study of such groups is both interesting in its own right, and can be applied to studying simple modules for simple groups, such as the sporadic groups in the final chapter. The fourth chapter analyzes the groups PSL(2,q); here we determine, in characteristic 2, which simple modules for PSL(2,q) are algebraic, for any odd q. The fifth chapter generalizes this analysis to many groups of Lie type, although most results here are in defining characteristic only. Notable exceptions include the small Ree groups, which have the 2-SMA property for all q. The sixth and final chapter focuses on the sporadic groups: for most groups we provide results on some simple modules, and some of the groups are completely analyzed in all characteristics. This is normally carried out by restricting to the Sylow p-subgroup. This thesis develops the current state of knowledge concerning algebraic modules for finite groups, and particularly for which simple groups, and for which primes, all simple modules are algebraic.

APA, Harvard, Vancouver, ISO, and other styles

Hutchinson, Samuel M. A. "The Morava cohomology of finite general linear groups." Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/20464/.

Full text

Abstract:

In this thesis, for all finite heights n and odd primes p, we compute the Morava E-theory and Morava K-theory of general linear groups over finite fields F of order q ≡ 1 mod p. We rephrase the problem in terms of V_*, the graded groupoid of vector spaces over F, and focus on the graded algebra and coalgebra structures induced from the direct sum functor. We use character theory to determine the ranks of E^0BV_* and K^0BV_*, and use this information to reverse engineer the Atiyah-Hirzebruch spectral sequence for K^*BV_* and K_*BV_*. We then use this result in two ways: we deduce that the algebra and coalgebra structures are free commutative and cofree cocommutative respectively, and we identify a lower bound for the nilpotence of the canonical top normalised Chern class in K^0BV_{p^k}. Following this we make use of algebro-geometric and Galois theoretic techniques to determine the indecomposables in Morava E-theory and K-theory, before using this calculation in conjunction with K-local duality and the nilpotence lower bound to determine the primitives of the coalgebra structure in Morava K-theory. Along the way, we show that E^0BV_* and K^0BV_* have structures similar to that of a graded Hopf ring, but with a modified version of the compatibility relation. We call such structures "graded faux Hopf rings".

APA, Harvard, Vancouver, ISO, and other styles

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

Full text

Abstract:

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 can be embedded as a subgroup of an M-group. After discussing results related to M-groups, we will construct explicit families of solvable groups that cannot be embedded as subnormal subgroups of any M-group. We also discuss groups possessing a unique non-monomial irreducible character, and prove that such a group cannot be simple.

APA, Harvard, Vancouver, ISO, and other styles

Bamblett, Jane Carswell. "Algorithms for computing in finite groups." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240616.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Brookes, Melanie. "On the efficiency of finite groups." Thesis, University of St Andrews, 1996. http://hdl.handle.net/10023/13682.

Full text

Abstract:

In Chapter 2 of this thesis we look at methods for finding efficient presentations of the transitive permutation groups of degree ≤ 12. Chapter 3 gives efficient presentations for certain direct products of groups including PSL(2, P)2 SL(2, p) X SL(2, 8), PSL(2, p) x C2, for prime p ≥ 5 and PSL(2, 25)3. Chapter 4 introduces a new class of inefficient groups and Chapter 5 gives a brief survey of some of the open problems relating to the efficiency of finite groups.

APA, Harvard, Vancouver, ISO, and other styles

Stavis, Andreas. "Representations of finite groups." Thesis, Karlstads universitet, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-69642.

Full text

Abstract:

Representation theory is concerned with the ways of writing elements of abstract algebraic structures as linear transformations of vector spaces. Typical structures amenable to representation theory are groups, associative algebras and Lie algebras. In this thesis we study linear representations of finite groups. The study focuses on character theory and how character theory can be used to extract information from a group. Prior to that, concepts needed to treat character theory, and some of their ramifications, are investigated. The study is based on existing literature, with excessive use of examples to illuminate important aspects. An example treating a class of p-groups is also discussed.

APA, Harvard, Vancouver, ISO, and other styles

Gutekunst, Todd M. "Subsets of finite groups exhibiting additive regularity." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 128 p, 2008. http://proquest.umi.com/pqdweb?did=1605136271&sid=5&Fmt=2&clientId=8331&RQT=309&VName=PQD.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Basu, Devjani. "A THESIS ON BLOCK THEORY FOR FINITE GROUPS." OpenSIUC, 2020. https://opensiuc.lib.siu.edu/theses/2721.

Full text

Abstract:

In this thesis, we relate the ordinary representation of a finite group, i.e. a representation over a field of characteristic $0$ to a representation over a field with characteristic $p$, called the modular representations, as, in the simplest of the sense, they are obtatined by reduction mod $p$. We are particularly interested in the situation, when $p$ divides the order of the group. This leads to the study of Brauer characters, decomposition matrix and eventually {\sl blocks} and its properties, along with a few enticing open conjectures related to blocks.

APA, Harvard, Vancouver, ISO, and other styles

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Marsh, Samual John. "The Morava E-theories of finite general linear groups." Thesis, University of Sheffield, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.505785.

Full text

Abstract:

By studying the representation theory of a certain infinite p-group and using the generalised characters of Hopkins, Kuhn and Ravenei we find useful ways of understanding the rational Morava E-theory of the classifying spaces of general linear groups over finite fields. Making use of the well understood theory of formal group laws we establish more subtle results integrally, building on relevant work of Tanabe. In particular, we study in detail the cases where the group has dimension less than or equal to the prime p at which the E-theory is localised.

APA, Harvard, Vancouver, ISO, and other styles

Brandt, Marco. "On unipotent Specht modules of finite general linear groups." [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11103979.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Ramiharimanana, Nantsoina Cynthia. "Realization of finite groups as Galois Groups over Q in Qtot,p." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85840.

Full text

APA, Harvard, Vancouver, ISO, and other styles

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

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

Ryten, Mark Jonathan. "Model theory of finite difference fields and simple groups." Thesis, University of Leeds, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.441226.

Full text

APA, Harvard, Vancouver, ISO, and other styles

McDougall-Bagnall, Jonathan M. "Generation problems for finite groups." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2529.

Full text

Abstract:

It can be deduced from the Burnside Basis Theorem that if G is a finite p-group with d(G)=r then given any generating set A for G there exists a subset of A of size r that generates G. We have denoted this property B. A group is said to have the basis property if all subgroups have property B. This thesis is a study into the nature of these two properties. Note all groups are finite unless stated otherwise. We begin this thesis by providing examples of groups with and without property B and several results on the structure of groups with property B, showing that under certain conditions property B is inherited by quotients. This culminates with a result which shows that groups with property B that can be expressed as direct products are exactly those arising from the Burnside Basis Theorem. We also seek to create a class of groups which have property B. We provide a method for constructing groups with property B and trivial Frattini subgroup using finite fields. We then classify all groups G where the quotient of G by the Frattini subgroup is isomorphic to this construction. We finally note that groups arising from this construction do not in general have the basis property. Finally we look at groups with the basis property. We prove that groups with the basis property are soluble and consist only of elements of prime-power order. We then exploit the classification of all such groups by Higman to provide a complete classification of groups with the basis property.

APA, Harvard, Vancouver, ISO, and other styles

Kleidman, Peter Brown. "The subgroup structure of some finite simple groups." Thesis, University of Cambridge, 1987. https://www.repository.cam.ac.uk/handle/1810/250910.

Full text

Abstract:

In this dissertation we completely determine the maximal subgroups of the following finite simple groups: (i) POgX?) and 3D^q) for all prime powers q (ii) 2G2(32m+1) for all integers m (iii) G2(<7) for all odd prime powers q. Moreover, if Go is one of the groups appearing in (i), (ii) or (iii), then we also determine the maximal subgroups of all groups G satisfying: GO

APA, Harvard, Vancouver, ISO, and other styles

Baccari, Charles. "Investigation of Finite Groups Through Progenitors." CSUSB ScholarWorks, 2017. https://scholarworks.lib.csusb.edu/etd/600.

Full text

Abstract:

The goal of this presentation is to find original symmetric presentations of finite groups. It is frequently the case, that progenitors factored by appropriate relations produce simple and even sporadic groups as homomorphic images. We have discovered two of the twenty-six sporadic simple groups namely, M12, J1 and the Lie type group Suz(8). In addition several linear and classical groups will also be presented. We will present several progenitors including: 2*12: 22 x (3 : 2), 2*11: PSL2(11), 2*5: (5 : 4) which have produced the homomorphic images: M12 : 2, Suz(8) x 2, and J1 x 2. We will give monomial progenitors whose homomorphic images are: 17*10 :m PGL2(9), 3*4:m Z2 ≀D4 , and 13*2:m (22 x 3) : 2 which produce the homomorphic images:132 : ((2 x 13) : (2 x 3)), 2 x S9, and (22)•PGL4(3). Once we have a presentation of a group we can verify the group's existence through double coset enumeration. We will give proofs of isomorphism types of the presented images: S3 x PGL2(7) x S5, 28:A5, and 2•U4(2):2.

APA, Harvard, Vancouver, ISO, and other styles

Turner, W. "Representations of finite general linear groups in non-describing characteristic." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393368.

Full text

APA, Harvard, Vancouver, ISO, and other styles

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

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Bastian, Nicholas Lee. "Terwilliger Algebras for Several Finite Groups." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/8897.

Full text

Abstract:

In this thesis, we will explore the structure of Terwilliger algebras over several different types of finite groups. We will begin by discussing what a Schur ring is, as well as providing many different results and examples of them. Following our discussion on Schur rings, we will move onto discussing association schemes as well as their properties. In particular, we will show every Schur ring gives rise to an association scheme. We will then define a Terwilliger algebra for any finite set, as well as discuss basic properties that hold for all Terwilliger algebras. After specializing to the case of Terwilliger algebras resulting from the orbits of a group, we will explore bounds of the dimension of such a Terwilliger algebra. We will also discuss the Wedderburn decomposition of a Terwilliger algebra resulting from the conjugacy classes of a group for any finite abelian group and any dihedral group.

APA, Harvard, Vancouver, ISO, and other styles

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.

Full text

Abstract:

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 subgroup lattice. The main body of this thesis is concerned with the behaviour of the subgroup permutability degree of the two families of finite simple groups PSL2(2n), and Sz(q). In both cases the subgroups of the two families of simple groups are completely known and we shall use this fact to establish that the subgroup permutability degree in each case vanishes asymptotically as n or q respectively tends to infinity. The final chapter of the thesis deviates from the main line to examine groups, called F-groups, which behave like nilpotent groups with respect to the Frattini subgroup of quotients. Finally, we present in the Appendix joint research on the distribution of the density of maximal order elements in general linear groups and offer code for computations in GAP related to permutability.

APA, Harvard, Vancouver, ISO, and other styles

Lee, Hyereem, and Hyereem Lee. "Triples in Finite Groups and a Conjecture of Guralnick and Tiep." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/624584.

Full text

Abstract:

In this thesis, we will see a way to use representation theory and the theory of linear algebraic groups to characterize certain family of finite groups. In Chapter 1, we see the history of preceding work. In particular, J. G. Thompson’s classification of minimal finite simple nonsolvable groups and characterization of solvable groups will be given. In Chapter 2, we will describe some background knowledge underlying this project and notation that will be widely used in this thesis. In Chapter 3, the main theorem originally conjectured by Guralnick and Tiep will be stated together with the base theorem which is a reduced version of main theorem to the case where we have a quasisimple group. Main theorem explains a way to characterize the finite groups with a composition factor of order divisible by two distinct primes p and q as the finite groups containing nontrivial 2-element x, p-element y, q-element z such that xyz = 1. In this thesis we more focus on the proof of showing a finite group G with a composition factor of order divisible by two distinct prime p and q contains nontrivial 2-element x, p-element y, q-element z such that xyz = 1. In Chapter 4, we will prove a set of lemmas and proposition which will be used as key tools in the proof of the base theorem. In Chapters 5 to 7, we will establish the base theorem in the cases where a quasisimple group G has its simple quotient isomorphic to alternating groups or sporadic groups (Chapter 5), classical groups (Chapter 6), and exceptional groups (Chapter 7). In Chapter 8, we show that any finite group G admitting nontrivial 2-element x, p- element y, q-element z such that xyz = 1 for two distinct odd primes p and q admits a composition factor of order divisible by pq. Also, we show that the question if a finite group G with a composition factor of order divisible by two distinct prime p and q contains nontrivial 2-element x, p-element y, q-element z such that xyz = 1 can be reduced to the base theorem.

APA, Harvard, Vancouver, ISO, and other styles

Horan, Katherine. "On the invariant theory of finite unipotent groups generated by bireflections." Thesis, University of Kent, 2017. https://kar.kent.ac.uk/65736/.

Full text

Abstract:

Let k be a field of characteristic p and let V be a k-vector space. In Chapter 2 of this thesis we classify all unipotent groups G ≤ GL(V ) consisting of bireflections for p not equal to 2: we show that unipotent groups consisting of bireflections are either two-row groups, two-column groups, hook groups or one of two types of exceptional group. The well known theorem of Chevalley-Shephard-Todd shows the importance of (pseudo-)reflection groups to invariant theory. Our interest in bireflection groups is motivated by the theorem of Kemper which tells us if G ≤ GL(V ) is a p-group and the invariant ring k[V ] G is Cohen-Macaulay then G is generated by bireflections. We use our classification to investigate which groups consisting of bireflections have Cohen-Macaulay or complete intersection invariant rings. In Chapter 3 we introduce techniques and notation which we use later to find invariant rings of groups by viewing them as subgroups of Nakajima groups. In Chapter 4 we show that for k = Fp there is a family of hook groups, including all non-abelian hook groups, which have complete intersection invariant rings. It is well known that Cohen-Macaulay invariant rings of p-groups in characteristic p are Gorenstein. There has been speculation by experts in the area, that they might in fact be complete intersections. In Chapter 5 we settle this negatively by giving an example of a p-group which has Cohen-Macaulay but non complete intersection invariant ring. To the best of our knowledge this is the first example of that kind. Finally in Chapter 6 we show that when k = F_p both types of exceptional group have complete intersection invariant rings.

APA, Harvard, Vancouver, ISO, and other styles

Kasouha, Abeir Mikhail. "Symmetric representations of elements of finite groups." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2605.

Full text

Abstract:

This thesis demonstrates an alternative, concise but informative, method for representing group elements, which will prove particularly useful for the sporadic groups. It explains the theory behind symmetric presentations, and describes the algorithm for working with elements represented in this manner.

APA, Harvard, Vancouver, ISO, and other styles

Berardinelli, Angela. "Restricting Invariants and Arrangements of Finite Complex Reflection Groups." Thesis, University of North Texas, 2015. https://digital.library.unt.edu/ark:/67531/metadc804919/.

Full text

Abstract:

Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism from the algebra of G-invariant polynomial functions on V to the algebra of C-invariant functions on X. In my thesis, I extend earlier work by Douglass and Röhrle for Coxeter groups to the case where G is a complex reflection group of type G(r,p,n) in the notation of Shephard and Todd and X is in the lattice of the reflection arrangement of G. The main result characterizes when the restriction mapping is surjective in terms of the exponents of G and C and their reflection arrangements.

APA, Harvard, Vancouver, ISO, and other styles

Wickramasekara, Sujeewa. "Differentiable representations of finite dimensional lie groups in rigged Hilbert spaces /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Wegner, Alexander. "The construction of finite soluble factor groups of finitely presented groups and its application." Thesis, University of St Andrews, 1992. http://hdl.handle.net/10023/12600.

Full text

Abstract:

Computational group theory deals with the design, analysis and computer implementation of algorithms for solving computational problems involving groups, and with the applications of the programs produced to interesting questions in group theory, in other branches of mathematics, and in other areas of science. This thesis describes an implementation of a proposal for a Soluble Quotient Algorithm, i.e. a description of the algorithms used and a report on the findings of an empirical study of the behaviour of the programs, and gives an account of an application of the programs. The programs were used for the construction of soluble groups with interesting properties, e.g. for the construction of soluble groups of large derived length which seem to be candidates for groups having efficient presentations. New finite soluble groups of derived length six with trivial Schur multiplier and efficient presentations are described. The methods for finding efficient presentations proved to be only practicable for groups of moderate order. Therefore, for a given derived length soluble groups of small order are of interest. The minimal soluble groups of derived length less than or equal to six are classified.

APA, Harvard, Vancouver, ISO, and other styles

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

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

Ward, David Charles. "Topics in finite groups : homology groups, pi-product graphs, wreath products and cuspidal characters." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/topics-in-finite-groups-homology-groups-piproduct-graphs-wreath-products-and-cuspidal-characters(7e90d219-fba7-4ff0-9071-c624acab7aaf).html.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Bartlett, Bruce. "On Unitary 2-representations of finite groups and topological quantum field theory." Thesis, University of Sheffield, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500530.

Full text

APA, Harvard, Vancouver, ISO, and other styles

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Yap, Ngee Thai. "Modeling syllable theory with finite-state transducers." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 279 p, 2006. http://proquest.umi.com/pqdweb?did=1179954391&sid=4&Fmt=2&clientId=8331&RQT=309&VName=PQD.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Ackermann, Bernd. "On the Loewy series of the Steinberg-PIM of finite general linear groups." [S.l.] : [s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11380460.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Gonda, Jessica Lynn. "Subgroups of Finite Wreath Product Groups for p=3." University of Akron / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=akron1460027790.

Full text

APA, Harvard, Vancouver, ISO, and other styles

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

Find full text

APA, Harvard, Vancouver, ISO, and other styles

De, Visscher Maud. "Some problems in the representation theory of reductive groups and their finite subgroups." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275506.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Starling, Charles B. "Actions of Finite Groups on Substitution Tilings and Their Associated C*-algebras." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/20663.

Full text

Abstract:

The goal of this thesis is to examine the actions of finite symmetry groups on aperiodic tilings. To an aperiodic tiling with finite local complexity arising from a primitive substitution rule one can associate a metric space, transformation groupoids, and C*-algebras. Finite symmetry groups of the tiling act on each of these objects and we investigate appropriate constructions on each, namely the orbit space, semidirect product groupoids, and crossed product C*-algebras respectively. Of particular interest are the crossed product C*-algebras; we derive important structure results about them and compute their K-theory.

APA, Harvard, Vancouver, ISO, and other styles

Prins, A. L. "Fischer-clifford matrices and character tables of inertia groups of maximal subgroups of finite simple groups of extension type." University of the Western Cape, 2011. http://hdl.handle.net/11394/5430.

Full text

Abstract:

Philosophiae Doctor - PhD
The aim of this dissertation is to calculate character tables of group extensions. There are several well–developed methods for calculating the character tables of group extensions. In this dissertation we study the method developed by Bernd Fischer, the so–called Fischer–Clifford matrices method, which derives its fundamentals from the Clifford theory. We consider only extensions G of the normal subgroup K by the subgroup Q with the property that every irreducible character of K can be extended to an irreducible character of its inertia group in G, if K is abelian. This is indeed the case if G is a split extension, by a well-known theorem of Mackey. A brief outline of the classical theory of characters pertinent to this study, is followed by a discussion on the calculation of the conjugacy classes of extension groups by the method of coset analysis. The Clifford theory which provide the basis for the theory of Fischer-Clifford matrices is discussed in detail. Some of the properties of these Fischer-Clifford matrices which make their calculation much easier are also given. As mentioned earlier we restrict ourselves to split extension groups G in which K is always elementary abelian. In this thesis we are concerned with the construction of the character tables of certain groups which are associated with Fi₂₂ and Sp₈ (2). Both of these groups have a maximal subgroup of the form 2⁷: Sp₆ (2) but they are not isomorphic to each other. In particular we are interested in the inertia groups of these maximal subgroups, which are split extensions. We use the technique of the Fischer-Clifford matrices to construct the character tables of these inertia groups. These inertia groups of 2⁷ : Sp₆(2), the maximal subgroup of Fi₂₂, are 2⁷ : S₈, 2⁷ : Ο⁻₆(2) and 2⁷ : (2⁵ : S₆). The inertia group of 2⁷ : Sp₆(2), the affine subgroup of Sp₈(2), is 2⁷ : (2⁵ : S₆) which is not isomorphic to the group with the same form which was mentioned earlier.

APA, Harvard, Vancouver, ISO, and other styles

Ferreira, Jorge Nélio Marques. "On invariant Rings of Sylow subgroups of finite classical groups." Doctoral thesis, University of Kent, 2011. http://hdl.handle.net/10400.13/177.

Full text

Abstract:

In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.

APA, Harvard, Vancouver, ISO, and other styles

Mahlasela, Zuko. "Finite fuzzy sets, keychains and their applications." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1005220.

Full text

Abstract:

The idea of keychains, an (n+1)-tuple of non-increasing real numbers in the unit interval always including 1, naturally arises in study of finite fuzzy set theory. They are a useful concept in modeling ideas of uncertainty especially those that arise in Economics, Social Sciences, Statistics and other subjects. In this thesis we define and study some basic properties of keychains with reference to Partially Ordered Sets, Lattices, Chains and Finite Fuzzy Sets. We then examine the role of keychains and their lattice diagrams in representing uncertainties that arise in such problems as in preferential voting patterns, outcomes of competitions and in Economics - Preference Relations.

APA, Harvard, Vancouver, ISO, and other styles

Nave, Lee Stewart. "The cohomology of finite subgroups of Morava stabilizer groups and Smith-Toda complexes /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5803.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Linton, Stephen Alexander. "The maximal subgroups of the sporadic groups Th, Fiâ†2â†4 and Fi'â†2â†4 and other topics." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.317925.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Yahiatene, Sophiane [Verfasser]. "Hurwitz action in Coxeter groups and extended Weyl groups with application in representation theory of finite dimensional algebras / Sophiane Yahiatene." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1222672243/34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Taylor, Jonathan. "On Unipotent Supports of Reductive Groups With a Disconnected Centre." Phd thesis, University of Aberdeen, 2012. http://tel.archives-ouvertes.fr/tel-00709051.

Full text

Abstract:

Let $\mathbf{G}$ be a connected reductive algebraic group defined over an algebraic closure of the finite field of prime order $p>0$, which we assume to be good for $\mathbf{G}$. We denote by $F : \mathbf{G} \to \mathbf{G}$ a Frobenius endomorphism of $\mathbf{G}$ and by $G$ the corresponding $\mathbb{F}_q$-rational structure. If $\operatorname{Irr}(G)$ denotes the set of ordinary irreducible characters of $G$ then by work of Lusztig and Geck we have a well defined map $\Phi_{\mathbf{G}} : \operatorname{Irr}(G) \to \{F\text{-stable unipotent conjugacy classes of }\mathbf{G}\}$ where $\Phi_{\mathbf{G}}(\chi)$ is the unipotent support of $\chi$.

Lusztig has given a classification of the irreducible characters of $G$ and obtained their degrees. In particular he has shown that for each $\chi \in \operatorname{Irr}(G)$ there exists an integer $n_{\chi}$ such that $n_{\chi}\cdot\chi(1)$ is a monic polynomial in $q$. Given a unipotent class $\mathcal{O}$ of $\mathbf{G}$ with representative $u \in \mathbf{G}$ we may define $A_{\mathbf{G}}(u)$ to be the finite quotient group $C_{\mathbf{G}}(u)/C_{\mathbf{G}}(u)^{\circ}$. If the centre $Z(\mathbf{G})$ is connected and $\mathbf{G}/Z(\mathbf{G})$ is simple then Lusztig and H\'zard have independently shown that for each $F$-stable unipotent class $\mathcal$ of $\mathbf$ there exists $\chi \in \operatorname(G)$ such that $\Phi_(\chi)=\mathcal$ and $n_ = |A_(u)|$, (in particular the map $\Phi_$ is surjective).

The main result of this thesis extends this result to the case where $\mathbf$ is any simple algebraic group, (hence removing the assumption that $Z(\mathbf)$ is connected). In particular if $\mathbf$ is simple we show that for each $F$-stable unipotent class $\mathcal$ of $\mathbf$ there exists $\chi \in \operatorname(G)$ such that $\Phi_(\chi) = \mathcal$ and $n_ = |A_(u)^F|$ where $u \in \mathcal^F$ is a well-chosen representative. We then apply this result to prove, (for most simple groups), a conjecture of Kawanaka's on generalised Gelfand--Graev representations (GGGRs). Namely that the GGGRs of $G$ form a $\mathbf{Z}$-basis for the $\mathbf{Z}$-module of all unipotently supported class functions of $G$. Finally we obtain an expression for a certain fourth root of unity associated to GGGRs in the case where $\mathbf{G}$ is a symplectic or special orthogonal group.

APA, Harvard, Vancouver, ISO, and other styles

Ngcibi, Sakhile Leonard. "Studies of equivalent fuzzy subgroups of finite abelian p-Groups of rank two and their subgroup lattices." Thesis, Rhodes University, 2006. http://hdl.handle.net/10962/d1005230.

Full text

Abstract:

We determine the number and nature of distinct equivalence classes of fuzzy subgroups of finite Abelian p-group G of rank two under a natural equivalence relation on fuzzy subgroups. Our discussions embrace the necessary theory from groups with special emphasis on finite p-groups as a step towards the classification of crisp subgroups as well as maximal chains of subgroups. Unique naming of subgroup generators as discussed in this work facilitates counting of subgroups and chains of subgroups from subgroup lattices of the groups. We cover aspects of fuzzy theory including fuzzy (homo-) isomorphism together with operations on fuzzy subgroups. The equivalence characterization as discussed here is finer than isomorphism. We introduce the theory of keychains with a view towards the enumeration of maximal chains as well as fuzzy subgroups under the equivalence relation mentioned above. We discuss a strategy to develop subgroup lattices of the groups used in the discussion, and give examples for specific cases of prime p and positive integers n,m. We derive formulas for both the number of maximal chains as well as the number of distinct equivalence classes of fuzzy subgroups. The results are in the form of polynomials in p (known in the literature as Hall polynomials) with combinatorial coefficients. Finally we give a brief investigation of the results from a graph-theoretic point of view. We view the subgroup lattices of these groups as simple, connected, symmetric graphs.

APA, Harvard, Vancouver, ISO, and other styles

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!