The Subgroup Structure Of The Finite Classical Groups
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The Subgroup Structure Of The Finite Classical Groups
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Author : Peter B. Kleidman
language : en
Publisher:
Release Date : 1990
The Subgroup Structure Of The Finite Classical Groups written by Peter B. Kleidman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Electronic books categories.
In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results.
The Subgroup Structure Of The Finite Classical Groups
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Author : Peter B. Kleidman
language : en
Publisher: Cambridge University Press
Release Date : 1990-04-26
The Subgroup Structure Of The Finite Classical Groups written by Peter B. Kleidman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-04-26 with Mathematics categories.
With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.
The Maximal Subgroups Of The Low Dimensional Finite Classical Groups
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Author : John N. Bray
language : en
Publisher: Cambridge University Press
Release Date : 2013-07-25
The Maximal Subgroups Of The Low Dimensional Finite Classical Groups written by John N. Bray and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-25 with Mathematics categories.
This book classifies the maximal subgroups of the almost simple finite classical groups in dimension up to 12; it also describes the maximal subgroups of the almost simple finite exceptional groups with socle one of Sz(q), G2(q), 2G2(q) or 3D4(q). Theoretical and computational tools are used throughout, with downloadable Magma code provided. The exposition contains a wealth of information on the structure and action of the geometric subgroups of classical groups, but the reader will also encounter methods for analysing the structure and maximality of almost simple subgroups of almost simple groups. Additionally, this book contains detailed information on using Magma to calculate with representations over number fields and finite fields. Featured within are previously unseen results and over 80 tables describing the maximal subgroups, making this volume an essential reference for researchers. It also functions as a graduate-level textbook on finite simple groups, computational group theory and representation theory.
The Subgroup Structure Of The Finite Classical Groups Peter Kleidman Martin Liebeck
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Author :
language : en
Publisher:
Release Date : 1990
The Subgroup Structure Of The Finite Classical Groups Peter Kleidman Martin Liebeck written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Classical Groups Derangements And Primes
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Author : Timothy C. Burness
language : en
Publisher: Cambridge University Press
Release Date : 2016-01-15
Classical Groups Derangements And Primes written by Timothy C. Burness and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-15 with Mathematics categories.
A graduate-level introduction to finite classical groups featuring a comprehensive account of the conjugacy and geometry of elements of prime order.
Linear Algebraic Groups And Finite Groups Of Lie Type
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Author : Gunter Malle
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08
Linear Algebraic Groups And Finite Groups Of Lie Type written by Gunter Malle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Mathematics categories.
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
Overgroups Of Root Groups In Classical Groups
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Author : Michael Aschbacher
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-26
Overgroups Of Root Groups In Classical Groups written by Michael Aschbacher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-26 with Mathematics categories.
The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of c-root subgroups.
Surveys In Combinatorics 2005
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Author : Bridget S. Webb
language : en
Publisher: Cambridge University Press
Release Date : 2005
Surveys In Combinatorics 2005 written by Bridget S. Webb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Combinatorial analysis categories.
This volume provides an up-to-date overview of current research across combinatorics.
The Irreducible Subgroups Of Exceptional Algebraic Groups
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Author : Adam R. Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18
The Irreducible Subgroups Of Exceptional Algebraic Groups written by Adam R. Thomas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.
This paper is a contribution to the study of the subgroup structure of excep-tional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we com-plete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected sub-group X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G.
Geometries And Groups
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Author : M. Aschbacher
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometries And Groups written by M. Aschbacher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The workshop was set up in order to stimulate the interaction between (finite and algebraic) geometries and groups. Five areas of concentrated research were chosen on which attention would be focused, namely: diagram geometries and chamber systems with transitive automorphism groups, geometries viewed as incidence systems, properties of finite groups of Lie type, geometries related to finite simple groups, and algebraic groups. The list of talks (cf. page iii) illustrates how these subjects were represented during the workshop. The contributions to these proceedings mainly belong to the first three areas; therefore, (i) diagram geometries and chamber systems with transitive automorphism groups, (ii) geometries viewed as incidence systems, and (iii) properties of finite groups of Lie type occur as section titles. The fourth and final section of these proceedings has been named graphs and groups; besides some graph theory, this encapsules most of the work related to finite simple groups that does not (explicitly) deal with diagram geometry. A few more words about the content: (i). Diagram geometries and chamber systems with transitive automorphism groups. As a consequence of Tits' seminal work on the subject, all finite buildings are known. But usually, in a situation where groups are to be characterized by certain data concerning subgroups, a lot less is known than the full parabolic picture corresponding to the building.