The Classification of Finite Simple Groups: Groups of Characteristic 2 Type (Mathematical Surveys and Monographs, 172) - Hardcover

Michael Aschbacher; Richard Lyons; Stephen D. Smith; Ronald Solomon

 
9780821853368: The Classification of Finite Simple Groups: Groups of Characteristic 2 Type (Mathematical Surveys and Monographs, 172)
Hardcover
ISBN 10: 0821853368 ISBN 13: 9780821853368
Publisher: American Mathematical Society, 2011

Synopsis

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.

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About the Author

Michael Aschbacher, California Institute of Technology, Pasadena, CA||Richard Lyons, Rutgers University, Piscataway, NJ|Stephen D. Smith, University of Illinois at Chicago, IL|Ronald Solomon, The Ohio State University, Columbus, O

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2011
Language
English
ISBN 10 
0821853368
ISBN 13 
9780821853368
Binding
Hardcover
Number of pages
347