Author : Gary M. Seitz
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 26,79 MB
Release : 1987
Category : Linear algebraic groups
ISBN : 0821824279
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.
Author : Peter B. Kleidman
Publisher : Cambridge University Press
Page : 317 pages
File Size : 12,58 MB
Release : 1990-04-26
Category : Mathematics
ISBN : 052135949X
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.
Author : John N. Bray
Publisher : Cambridge University Press
Page : 453 pages
File Size : 38,68 MB
Release : 2013-07-25
Category : Mathematics
ISBN : 1107276225
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.
Author : Gunter Malle
Publisher : Cambridge University Press
Page : 324 pages
File Size : 30,74 MB
Release : 2011-09-08
Category : Mathematics
ISBN : 113949953X
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.
Author : Meinolf Geck
Publisher : Oxford University Press
Page : 321 pages
File Size : 25,79 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 019967616X
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.
Author : J. S. Milne
Publisher : Cambridge University Press
Page : 665 pages
File Size : 20,85 MB
Release : 2017-09-21
Category : Mathematics
ISBN : 1107167485
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Author : R.W. Carter
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 26,75 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9401153086
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.
Author : Martin W. Liebeck
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 47,93 MB
Release : 1996
Category : Mathematics
ISBN : 0821804618
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.
Author : Martin W. Liebeck
Publisher : Cambridge University Press
Page : 505 pages
File Size : 41,1 MB
Release : 1992-09-10
Category : Mathematics
ISBN : 0521406854
This volume contains a collection of papers on the subject of the classification of finite simple groups.
Author : Richard S. Elman
Publisher : American Mathematical Soc.
Page : 215 pages
File Size : 48,20 MB
Release : 1993
Category : Mathematics
ISBN : 0821851616
* 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.
