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OverviewAfter 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. Full Product DetailsAuthor: Daniel Gorenstein , Ronald SolomonPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 40 Weight: 0.827kg ISBN: 9780821813799ISBN 10: 082181379 Pages: 341 Publication Date: 30 March 1999 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsGeneral lemmas Strongly embedded subgroups and related conditions on involutions $p$-component uniqueness theorems Properties of $K$-groups Background references Expository references Errata for number 3, Chapter I$_A$: Almost simple $\mathcal K$-groups Glossary Index of terminology.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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