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The Maximal Subgroups Of Classical Algebraic Groups
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Book Synopsis The Maximal Subgroups of Classical Algebraic Groups by : Gary M. Seitz
Download or read book The Maximal Subgroups of Classical Algebraic Groups written by Gary M. Seitz and published by American Mathematical Soc.. This book was released on 1987 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let [italic]V be a finite dimensional vector space over an algebraically closed field of characteristic p [greater than] 0 and let G = SL([italic]V), Sp([italic]V), or SO([italic]V). The main result describes all closed, connected, overgroups of [italic]X in SL([italic]V), assuming [italic]X is a closed, connected, irreducible subgroup of G.
Book Synopsis The Subgroup Structure of the Finite Classical Groups by : Peter B. Kleidman
Download or read book The Subgroup Structure of the Finite Classical Groups written by Peter B. Kleidman and published by Cambridge University Press. This book was released on 1990-04-26 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Linear Algebraic Groups and Finite Groups of Lie Type by : Gunter Malle
Download or read book Linear Algebraic Groups and Finite Groups of Lie Type written by Gunter Malle and published by Cambridge University Press. This book was released on 2011-09-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Maximal Subgroups of the Low-Dimensional Finite Classical Groups by : John N. Bray
Download or read book The Maximal Subgroups of the Low-Dimensional Finite Classical Groups written by John N. Bray and published by Cambridge University Press. This book was released on 2013-07-25 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Algebraic Geometry and Algebraic Groups by : Meinolf Geck
Download or read book An Introduction to Algebraic Geometry and Algebraic Groups written by Meinolf Geck and published by Oxford University Press. This book was released on 2013-03-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
Download or read book Algebraic Groups written by J. S. Milne and published by Cambridge University Press. This book was released on 2017-09-21 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Book Synopsis Algebraic Groups and their Representations by : R.W. Carter
Download or read book Algebraic Groups and their Representations written by R.W. Carter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.
Book Synopsis Reductive Subgroups of Exceptional Algebraic Groups by : Martin W. Liebeck
Download or read book Reductive Subgroups of Exceptional Algebraic Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 1996 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of simple algebraic groups is important in many areas of mathematics. The authors of this book investigate the subgroups of certain types of simple algebraic groups and obtain a complete description of all those subgroups which are themselves simple. This description is particularly useful in understanding centralizers of subgroups and restrictions of representations.
Book Synopsis Groups, Combinatorics and Geometry by : Martin W. Liebeck
Download or read book Groups, Combinatorics and Geometry written by Martin W. Liebeck and published by Cambridge University Press. This book was released on 1992-09-10 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers on the subject of the classification of finite simple groups.
Book Synopsis Linear Algebraic Groups and Their Representations by : Richard S. Elman
Download or read book Linear Algebraic Groups and Their Representations written by Richard S. Elman and published by American Mathematical Soc.. This book was released on 1993 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Brings together a wide variety of themes under a single unifying perspective The proceedings of a conference on Linear algebraic Groups and their Representations - the text gets to grips with the fundamental nature of this subject and its interaction with a wide variety of active areas in mathematics and physics.
Book Synopsis Groups St Andrews 2017 in Birmingham by : C. M. Campbell
Download or read book Groups St Andrews 2017 in Birmingham written by C. M. Campbell and published by Cambridge University Press. This book was released on 2019-04-11 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.
Book Synopsis The Irreducible Subgroups of Exceptional Algebraic Groups by : Adam R. Thomas
Download or read book The Irreducible Subgroups of Exceptional Algebraic Groups written by Adam R. Thomas and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups by : Martin W. Liebeck
Download or read book The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2004 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intends to complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This title follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.
Book Synopsis Geometries and Groups by : M. Aschbacher
Download or read book Geometries and Groups written by M. Aschbacher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Proceedings of the St. Petersburg Mathematical Society, Volume I by : O. A. Ladyzhenskaya Anatoli_ Moiseevich Vershik
Download or read book Proceedings of the St. Petersburg Mathematical Society, Volume I written by O. A. Ladyzhenskaya Anatoli_ Moiseevich Vershik and published by American Mathematical Soc.. This book was released on 1993-03-22 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the inaugural volume of a new book series published under the auspices of the St. Petersburg Mathematical Society. The book contains contributions by some of the leading mathematicians in St. Petersburg. Ranging over a wide array of topics, these papers testify to the diverse interests and productive mathematical life of the St. Petersburg Mathematical Society.
Book Synopsis Multiplicity-free Representations of Algebraic Groups by : Martin W. Liebeck
Download or read book Multiplicity-free Representations of Algebraic Groups written by Martin W. Liebeck and published by American Mathematical Society. This book was released on 2024-03-18 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Proceedings of the International Conference on Algebra Dedicated to the Memory of A. I. Mal$'$cev by : Leonid A. Bokut'
Download or read book Proceedings of the International Conference on Algebra Dedicated to the Memory of A. I. Mal$'$cev written by Leonid A. Bokut' and published by American Mathematical Soc.. This book was released on 1992 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt:
