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Mathematical Surveys and Monographs
1999; 341 pp; hardcover
List Price: US$92
Member Price: US$73.60
Order Code: SURV/40.4
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.
Graduate students and research mathematicians working in group theory and generalizations.
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