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Author: Ross Lawther
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 146
ISBN-13: 0821819666
DOWNLOAD EBOOKThis book is intended for graduate students and research mathematicians interested in group theory and genralizations
Author: Adam R. Thomas
Publisher: American Mathematical Soc.
Published: 2021-06-18
Total Pages: 191
ISBN-13: 1470443376
DOWNLOAD EBOOKThis 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.
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 122
ISBN-13: 0821804618
DOWNLOAD EBOOKThe 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: Alastair J. Litterick
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 168
ISBN-13: 1470428377
DOWNLOAD EBOOKThe study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.
Author: Gary M. Seitz
Publisher: American Mathematical Soc.
Published: 1991
Total Pages: 205
ISBN-13: 0821825046
DOWNLOAD EBOOKLet [italic]G be a simple algebraic group of exceptional type over an algebraically closed field of characteristic [italic]p. The subgroups of [italic]G maximal with respect to being closed and connected are determined, although mild restrictions on [italic]p are required in dealing with certain simple subgroups of low rank. For [italic]p = 0 we recover the results of Dynkin.
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 242
ISBN-13: 0821834827
DOWNLOAD EBOOKIntends 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.
Author: David A. Craven
Publisher: American Mathematical Society
Published: 2022-04-08
Total Pages: 168
ISBN-13: 1470451190
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Author: R.W. Carter
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 388
ISBN-13: 9401153086
DOWNLOAD EBOOKThis 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: B. Hartley
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 469
ISBN-13: 9401103291
DOWNLOAD EBOOKThis volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni
Author: Roger W. Carter
Publisher: Cambridge University Press
Published: 1998-09-03
Total Pages: 203
ISBN-13: 0521643252
DOWNLOAD EBOOKThis volume provides a very accessible introduction to the representation theory of reductive algebraic groups.
