**Mathematical Surveys and Monographs**

Volume: 40;
1996;
218 pp;
Hardcover

MSC: Primary 20;

Print ISBN: 978-0-8218-0390-5

Product Code: SURV/40.2

List Price: $80.00

AMS Member Price: $64.00

MAA Member Price: $72.00

**Electronic ISBN: 978-0-8218-3376-6
Product Code: SURV/40.2.E**

List Price: $75.00

AMS Member Price: $60.00

MAA Member Price: $67.50

#### Supplemental Materials

# The Classification of the Finite Simple Groups, Number 2

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*Daniel Gorenstein; Richard Lyons; Ronald Solomon*

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.

#### Readership

Advanced graduate students and mathematicians who specialize in finite group theory.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## The Classification of the Finite Simple Groups, Number 2

- Contents ix10 free
- Preface xi12 free
- Part I, Chapter G: General Group Theory 114 free
- A. Introduction 114
- B. Semisimple Subgroups 619
- C. Nilpotent Groups and Their Extensions 5366
- D. Fusion and Normal Subgroups 89102
- E. Uniqueness Subgroups 101114
- F. The Analysis of Signalizers 110123
- G. Subgroups of Parabolic Type 134147
- H. Some Recognition Issues 169182
- I. Characters and Counting 188201

- Background References 203216
- Expository References 204217
- Glossary 207220
- Index 210223