3-Transposition Groups PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download 3-Transposition Groups PDF full book. Access full book title 3-Transposition Groups by Michael Aschbacher. Download full books in PDF and EPUB format.
Author: Michael Aschbacher
Publisher: Cambridge University Press
ISBN: 9780521571968
Category : Mathematics
Languages : en
Pages : 276
Get Book Here
Book Description
Contains the first complete published proof of Fischer's Theorem on the classification of 3-transposition groups.
Author: Michael Aschbacher
Publisher: Cambridge University Press
ISBN: 9780521571968
Category : Mathematics
Languages : en
Pages : 276
Get Book Here
Book Description
Contains the first complete published proof of Fischer's Theorem on the classification of 3-transposition groups.
Author: Martin W. Liebeck
Publisher: Cambridge University Press
ISBN: 0521406854
Category : Mathematics
Languages : en
Pages : 505
Get Book Here
Book Description
This volume contains a collection of papers on the subject of the classification of finite simple groups.
Author: Alexander A. Ivanov
Publisher: Cambridge University Press
ISBN: 1009338056
Category : Mathematics
Languages : en
Pages : 584
Get Book Here
Book Description
Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
Author: Manjul Bhargava
Publisher: American Mathematical Soc.
ISBN: 1470436787
Category : Biography & Autobiography
Languages : en
Pages : 242
Get Book Here
Book Description
Classification 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: Michael Aschbacher
Publisher: American Mathematical Soc.
ISBN: 1470418452
Category : Mathematics
Languages : en
Pages : 196
Get Book Here
Book Description
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.
Author: Robert Wilson
Publisher: Springer Science & Business Media
ISBN: 1848009887
Category : Mathematics
Languages : en
Pages : 310
Get Book Here
Book Description
Thisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].
Author: Aleksandr Anatolievich Ivanov
Publisher: Cambridge University Press
ISBN: 0521889944
Category : Mathematics
Languages : en
Pages : 267
Get Book Here
Book Description
A rigorous construction and uniqueness proof for the Monster group, detailing its relation to Majorana involutions.
Author: Bernd Fischer
Publisher:
ISBN:
Category : Finite groups
Languages : en
Pages : 188
Get Book Here
Book Description
Author: M. Aschbacher
Publisher: Springer Science & Business Media
ISBN: 9400940173
Category : Mathematics
Languages : en
Pages : 533
Get Book Here
Book Description
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.
Author: Michael Aschbacher
Publisher: Cambridge University Press
ISBN: 9780521420495
Category : Mathematics
Languages : en
Pages : 336
Get Book Here
Book Description
Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates that each finite simple group is either a finite analogue of a simple Lie group or one of 26 pathological sporadic groups. Sporadic Groups provides for the first time a self-contained treatment of the foundations of the theory of sporadic groups accessible to mathematicians with a basic background in finite groups such as in the author's text Finite Group Theory. Introductory material useful for studying the sporadics, such as a discussion of large extraspecial 2-subgroups and Tits' coset geometries, opens the book. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows. The Golay and Todd modules, and the 2-local geometry for M24 are discussed. This is followed by the standard construction of Conway of the Leech lattice and the Conway group. The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits, plus a few new wrinkles. Researchers in finite group theory will find this text invaluable. The subjects treated will interest combinatorists, number theorists, and conformal field theorists.
