The Classification of the Finite Simple Groups, Number Four: Part 11, Chapters 1-4: Uniqueness Theorems: Uniqueness Theorems No.4 (Mathematical Surveys and Monographs) - Hardcover

Gorenstein, Daniel; Lyons, Richard; Solomon, Ronald

Hardcover

ISBN 10: 082181379X ISBN 13: 9780821813799

Publisher: American Mathematical Society, 1999

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1999
• ISBN 10: 082181379X
• ISBN 13: 9780821813799
• Binding: Hardcover
• Language: English