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Author: John N. Bray
Publisher: Cambridge University Press
Published: 2013-07-25
Total Pages: 453
ISBN-13: 0521138604
DOWNLOAD EBOOKClassifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.
Author: John N. Bray
Publisher: Cambridge University Press
Published: 2013-07-25
Total Pages: 453
ISBN-13: 1107276225
DOWNLOAD EBOOKThis 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: Peter B. Kleidman
Publisher: Cambridge University Press
Published: 1990-04-26
Total Pages: 317
ISBN-13: 052135949X
DOWNLOAD EBOOKWith 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: Bridget S. Webb
Publisher: Cambridge University Press
Published: 2005-07-21
Total Pages: 270
ISBN-13: 9780521615235
DOWNLOAD EBOOKThis volume provides an up-to-date overview of current research across combinatorics,.
Author: Manjul Bhargava
Publisher: American Mathematical Soc.
Published: 2017-07-24
Total Pages: 242
ISBN-13: 1470436787
DOWNLOAD EBOOKClassification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.
Author: O. A. Ladyzhenskaya Anatoli_ Moiseevich Vershik
Publisher: American Mathematical Soc.
Published: 1993-03-22
Total Pages: 244
ISBN-13: 9780821895900
DOWNLOAD EBOOKThis 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.
Author: Scott Harper
Publisher: Springer Nature
Published: 2021-05-25
Total Pages: 154
ISBN-13: 3030741001
DOWNLOAD EBOOKThis monograph studies generating sets of almost simple classical groups, by bounding the spread of these groups. Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group, every nontrivial element belongs to a generating pair. Groups with this property are said to be 3/2-generated. Breuer, Guralnick and Kantor conjectured that a finite group is 3/2-generated if and only if every proper quotient is cyclic. We prove a strong version of this conjecture for almost simple classical groups, by bounding the spread of these groups. This involves analysing the automorphisms, fixed point ratios and subgroup structure of almost simple classical groups, so the first half of this monograph is dedicated to these general topics. In particular, we give a general exposition of Shintani descent. This monograph will interest researchers in group generation, but the opening chapters also serve as a general introduction to the almost simple classical groups.
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
Published: 1990
Total Pages: 161
ISBN-13: 0821824945
DOWNLOAD EBOOKThe main result describes completely the maximal factorizations of all the finite simple groups and their automorphism groups. As a consequence, a classification of the maximal subgroups of the finite alternating and symmetric groups is obtained.
Author: Konrad K. Dabrowski
Publisher: Cambridge University Press
Published: 2021-06-24
Total Pages: 379
ISBN-13: 1009018884
DOWNLOAD EBOOKThese nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.
Author: Nick Gill
Publisher: Springer Nature
Published: 2022-06-17
Total Pages: 221
ISBN-13: 3030959562
DOWNLOAD EBOOKThis book gives a proof of Cherlin’s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan’s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. The first part gives a full introduction to Cherlin’s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest to a wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.
