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The Classification of the Finite Simple Groups, Number 2
Daniel Gorenstein, Richard Lyons, Rutgers University, New Brunswick, NJ, and Ronald Solomon, Ohio State University, Columbus, OH
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Mathematical Surveys and Monographs
1996; 218 pp; hardcover
Volume: 40
ISBN-10: 0-8218-0390-5
ISBN-13: 978-0-8218-0390-5
List Price: US$71 Member Price: US$56.80
Order Code: SURV/40.2

The Classification Theorem is one of the main achievements of 20th century mathematics, but its proof has not yet been completely extricated from the journal literature in which it first appeared. This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important subgroups.

The sections on semisimple subgroups and subgroups of parabolic type give detailed treatments of these important subgroups, including some results not available until now or available only in journal literature. The signalizer section provides an extensive development of both the Bender Method and the Signalizer Functor Method, which play a central role in the proof of the Classification Theorem.

This book would be a valuable companion text for a graduate group theory course.

Reviews

"A model of clarity and precision ... contains many gems of exposition and new proofs ... makes clear the very questions that could revolutionize the proof."

-- Mathematical Reviews

"Apart from readers studying the classification theorem in some detail, this volume is also of interest to someone who just wants to get acquainted with some of the principal methods of the classification theorem but does not want to follow the long proof itself."

-- Zentralblatt MATH

"The authors are among the best expositors in finite group theory. Their treatment of all these topics is clear and elegant ... gives an attractive treatment of local group theory ... should be in the library of all finite group theorists."

-- Bulletin of the AMS