The Classification of the Finite Simple Groups, Number 4 (Mathematical Surveys and Monographs) (No.4) [Hardcover]

Daniel Gorenstein (Author), Richard Lyons (Author), Ronald Solomon (Author)

Book Description

Publication Date: March 16, 1999 | ISBN-10: 082181379X | ISBN-13: 978-0821813799

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.

Editorial Reviews

Review

This series of volumes ... is a model for all mathematicians of the standards and clarity that should be achieved. --Mathematical Reviews

Product Details

• Hardcover: 341 pages
• Publisher: American Mathematical Society (March 16, 1999)
• Language: English
• ISBN-10: 082181379X
• ISBN-13: 978-0821813799
• Product Dimensions: 10.1 x 7.2 x 0.9 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #4,499,782 in Books (See Top 100 in Books)