The Classification of the Finite Simple Groups: Part II, Chapter G : General group theory (Mathematical Surveys and Monographs)
by: Daniel Gorenstein Richard Lyons Ronald Solomon
The Classification of the Finite Simple Groups: Part Ii, Chapter G : General Group Theory (Mathematical Surveys and Monographs)
By: Daniel Gorenstein Richard Lyons Ronald Solomon
ISBN-10: 0821803905 ISBN-13: 9780821803905
Publisher: American Mathematical Society - 1996-08
ISBNs of this book
Hardcover: 0821803905 1996, 1rst Edition (According to Amazon.com published on August 1996, According to Barnes & Noble published on October 1995)
Hardcover: 0821827766 June 2002, 1rst Edition Reprint (June 2002, according to all sources)
Book Description
The Classification Theorem is one of the main achievements of 20th century mathematics, but its proof has not yet been completely extricated from the journal literature in which it first appeared. This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important subgroups.
The sections on semisimple subgroups and subgroups of parabolic type give detailed treatments of these important subgroups, including some results not available until now or available only in journal literature. The signalizer section provides an extensive development of both the Bender Method and the Signalizer Functor Method, which play a central role in the proof of the Classification Theorem.
This book would be a valuable companion text for a graduate group theory course.
Table of Contents:
Frontmatter
* Title
* Copyright Page
* Dedication
* Table of Contents
* Preface
1. Introduction
2. Semisimple Subgroups
3. Nilpotent Groups and Their Extensions
4. Fusion and Normal Subgroups
5. Uniqueness Subgroups
6. The Analysis of Signalizers
7. Subgroups of Parabolic Type
8. Some Recognition Issues
9. Characters and Counting
Endmatter
* Background References
* Expository References
* Glossary
* Index
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