The Classification of Finite Simple Groups: Groups of Characteristic 2 Type

The Classification of Finite Simple Groups: Groups of Characteristic 2 Type
ISBN-10
0821853368
ISBN-13
9780821853368
Category
Finite simple groups
Pages
347
Language
English
Published
2011
Publisher
American Mathematical Soc.
Authors
Stephen D. Smith, Michael Aschbacher, Richard Lyons

Description

The book provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the "even case", where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of "noncharacteristic 2 type". However, this book provides much more. Chapter 0 is a modern overview of the logical structure of the entire classification. Chapter 1 is a concise but complete outline of the "odd case" with updated references, while Chapter 2 sets the stage for the remainder of the book with a similar outline of the "even case". The remaining six chapters describe in detail the fundamental results whose union completes the proof of the classification theorem. Several important subsidiary results are also discussed. In addition, there is a comprehensive listing of the large number of papers referenced from the literature. Appendices provide a brief but valuable modern introduction to many key ideas and techniques of the proof. Some improved arguments are developed, along with indications of new approaches to the entire classification--such as the second and third generation projects--although there is no attempt to cover them comprehensively. The work should appeal to a broad range of mathematicians--from those who just want an overview of the main ideas of the classification, to those who want a reader's guide to help navigate some of the major papers, and to those who may wish to improve the existing proofs.

Get the book

Amazon.com
Amazon.com
Search the book
eBay.com
eBay.com
Search the book

Other editions

Similar books

  • The Classification of the Finite Simple Groups, Number 2
    The Classification of the Finite Simple Groups, Number 2
    By Richard Lyons, Ronald Solomon, Daniel Gorenstein

    We begin with the basic Three Subgroups Lemma , which is a direct consequence of Philip Hall's Jacobi - like commutator ... B , C are subgroups of X and N X with ( A , B , C ) < N and ( C , A , B ) < N , then ( B , C , A ] < N. PROOF .

  • Applying the Classification of Finite Simple Groups: A User’s Guide
    Applying the Classification of Finite Simple Groups: A User’s Guide
    By Stephen D. Smith

    MR916173 Martin W. Liebeck, Cheryl E. Praeger, and Jan Saxl, On the O'Nan-Scott theorem for finite primitive permutation groups, J. Austral. Math. Soc. Ser. A 44 (1988), no. 3, 389–396. MR929529 Vicente Landazuri and Gary M. Seitz,&nbsp;...

  • The classification of the finite simple groups
    The classification of the finite simple groups
    By Richard Lyons, Daniel Gorenstein

    If A E EX + 2 ( G ) , k a positive integer , and G is ( k + 1 ) -balanced with respect to A , then TA , k + 1 ( G ) ... to be able to verify either k - balance or ( k + 2 ) -balance with respect to A. As shown by Gorenstein and Walter&nbsp;...

  • The Classification of the Finite Simple Groups, Number 7: Part III, Chapters 7–11
    The Classification of the Finite Simple Groups, Number 7: Part III, Chapters 7–11
    By Ronald Solomon, Daniel Gorenstein, Richard Lyon

    Now J is (a, y)-invariant and by L3-balance, J is the product of one or three (a, y)-conjugate components with Kf and Laf being ... Therefore J is a single 3-component, simultaneously a pumpup of Kf and of Laf. ... Hence, Adla = 3.