**Mathematical Surveys and Monographs**

Volume: 172;
2011;
347 pp;
Hardcover

MSC: Primary 20;

Print ISBN: 978-0-8218-5336-8

Product Code: SURV/172

List Price: $99.00

Individual Member Price: $79.20

**Electronic ISBN: 978-1-4704-1399-6
Product Code: SURV/172.E**

List Price: $99.00

Individual Member Price: $79.20

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#### Supplemental Materials

# The Classification of Finite Simple Groups: Groups of Characteristic 2 Type

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*Michael Aschbacher; Richard Lyons; Stephen D. Smith; Ronald Solomon*

The book provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the “even case”, where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of “noncharacteristic 2 type”.

However, this book provides much more. Chapter 0 is a modern overview of the logical structure of the entire classification. Chapter 1 is a concise but complete outline of the “odd case” with updated references, while Chapter 2 sets the stage for the remainder of the book with a similar outline of the “even case”. The remaining six chapters describe in detail the fundamental results whose union completes the proof of the classification theorem. Several important subsidiary results are also discussed. In addition, there is a comprehensive listing of the large number of papers referenced from the literature. Appendices provide a brief but valuable modern introduction to many key ideas and techniques of the proof. Some improved arguments are developed, along with indications of new approaches to the entire classification—such as the second and third generation projects—although there is no attempt to cover them comprehensively.

The work should appeal to a broad range of mathematicians—from those who just want an overview of the main ideas of the classification, to those who want a reader's guide to help navigate some of the major papers, and to those who may wish to improve the existing proofs.

#### Table of Contents

# Table of Contents

## The Classification of Finite Simple Groups: Groups of Characteristic 2 Type

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xi12 free
- Part I. Background and overview 114 free
- Introduction 316
- Overview: The classification of groups of Gorenstein-Walter type 2538
- Overview: The classification of groups of characteristic 2 type 6376
- Part II. Outline of the classification of groups of characteristic 2 type 8396
- 𝑒(𝐺)≤2: The classification of quasithin groups 8598
- 𝑒(𝐺)=3: The classification of rank 3 groups 127140
- 𝑒(𝐺)≥4: The pretrichotomy and trichotomy theorems 149162
- The classification of groups of standard type 173186
- The classification of groups of 𝐺𝐹(2) type 183196
- The final contradiction: Eliminating the Uniqueness Case 213226
- Part III. Appendices 249262
- Some background material related to simple groups 251264
- Overview of some techniques used in the classification 267280
- Part IV. References and index 313326
- References used for both 𝐺𝑊 type and characteristic 2 type 315328
- References mainly for 𝐺𝑊 type 317330
- References used primarily for characteristic 2 type 321334
- Expository references mentioned 329342
- Index 333346 free
- Back Cover Back Cover1362

#### Readership

Graduate students and research mathematicians interested in classification of finite simple groups.