The Classification of the Finite Simple Groups: Uniqueness Theorems

The Classification of the Finite Simple Groups: Uniqueness Theorems

by Daniel Gorenstein, Ronald Solomon, Richard Lyons, Ronald Solomon
     
 

ISBN-10: 082181379X

ISBN-13: 9780821813799

Pub. Date: 01/01/1999

Publisher: American Mathematical Society

After three introductory volumes on the classification of the finite simple groups, (Mathematical Surveys and Monographs, Volumes 40.1, 40.2, and 40.3), the authors now start the proof of the classification theorem: They begin the analysis of a minimal counterexample $G$ to the theorem. Two fundamental and powerful theorems in finite group theory are

Overview

After three introductory volumes on the classification of the finite simple groups, (Mathematical Surveys and Monographs, Volumes 40.1, 40.2, and 40.3), the authors now start the proof of the classification theorem: They begin the analysis of a minimal counterexample $G$ to the theorem. Two fundamental and powerful theorems in finite group theory are examined: the Bender-Suzuki theorem on strongly embedded subgroups (for which the non-character-theoretic part of the proof is provided) and Aschbacher's Component theorem. Included are new generalizations of Aschbacher's theorem which treat components of centralizers of involutions and $p$-components of centralizers of elements of order $p$ for arbitrary primes $p$. This book, with background from sections of the previous volumes, presents in an approachable manner critical aspects of the classification of finite simple groups. Features: Treatment of two fundamental and powerful theorems in finite group theory. Proofs that are accessible and largely self-contained. New results generalizing Aschbacher's Component theorem and related component uniqueness theorems.

Product Details

ISBN-13:
9780821813799
Publisher:
American Mathematical Society
Publication date:
01/01/1999
Series:
Mathematical Surveys and Monographs Series, #40
Pages:
341

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