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

Michael Aschbacher California Institute of Technology, Pasadena, CA
Richard Lyons Rutgers University, Piscataway, NJ
Stephen D. Smith University of Illinois at Chicago, Chicago, IL
Ronald Solomon The Ohio State University, Columbus, OH
Available Formats:
Hardcover ISBN: 978-0-8218-5336-8
Product Code: SURV/172
List Price: $105.00 MAA Member Price:$94.50
AMS Member Price: $84.00 Electronic ISBN: 978-1-4704-1399-6 Product Code: SURV/172.E List Price:$99.00
MAA Member Price: $89.10 AMS Member Price:$79.20
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AMS Member Price: $126.00 Click above image for expanded view The Classification of Finite Simple Groups: Groups of Characteristic 2 Type Michael Aschbacher California Institute of Technology, Pasadena, CA Richard Lyons Rutgers University, Piscataway, NJ Stephen D. Smith University of Illinois at Chicago, Chicago, IL Ronald Solomon The Ohio State University, Columbus, OH Available Formats:  Hardcover ISBN: 978-0-8218-5336-8 Product Code: SURV/172  List Price:$105.00 MAA Member Price: $94.50 AMS Member Price:$84.00
 Electronic ISBN: 978-1-4704-1399-6 Product Code: SURV/172.E
 List Price: $99.00 MAA Member Price:$89.10 AMS Member Price: $79.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$157.50 MAA Member Price: $141.75 AMS Member Price:$126.00
• Book Details

Mathematical Surveys and Monographs
Volume: 1722011; 347 pp
MSC: Primary 20;

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.

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

• Background and overview
• 0. Introduction
• 1. Overview: The classification of groups of Gorenstein-Walter type
• 2. Overview: The classification of groups of characteristic 2 type
• Outline of the classification of groups of characteristic 2 type
• 3. $e(G)\leq 2$: The classification of quasithin groups
• 4. $e(G)=3$: The classification of rank 3 groups
• 5. $e(G)\geq 4$: The pretrichotomy and trichotomy theorems
• 6. The classification of groups of standard type
• 7. The classification of groups of $GF(2)$ type
• 8. The final contradiction: Eliminating the Uniqueness Case
• Appendices
• A. Some background material related to simple groups
• B. Overview of some techniques used in the classification

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1722011; 347 pp
MSC: Primary 20;

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.

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

• Background and overview
• 0. Introduction
• 1. Overview: The classification of groups of Gorenstein-Walter type
• 2. Overview: The classification of groups of characteristic 2 type
• Outline of the classification of groups of characteristic 2 type
• 3. $e(G)\leq 2$: The classification of quasithin groups
• 4. $e(G)=3$: The classification of rank 3 groups
• 5. $e(G)\geq 4$: The pretrichotomy and trichotomy theorems
• 6. The classification of groups of standard type
• 7. The classification of groups of $GF(2)$ type
• 8. The final contradiction: Eliminating the Uniqueness Case
• Appendices
• A. Some background material related to simple groups
• B. Overview of some techniques used in the classification
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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