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The classification of the finite simple groups
 
Richard Lyons Rutgers University, New Brunswick, NJ
Ronald Solomon Ohio State University, Columbus, OH
The classification of the finite simple groups
Softcover ISBN:  978-0-8218-0960-0
Product Code:  SURV/40.1.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $77.40
eBook ISBN:  978-1-4704-1267-8
Product Code:  SURV/40.1.S.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $75.00
Softcover ISBN:  978-0-8218-0960-0
eBook: ISBN:  978-1-4704-1267-8
Product Code:  SURV/40.1.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $152.40 $114.90
The classification of the finite simple groups
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The classification of the finite simple groups
Richard Lyons Rutgers University, New Brunswick, NJ
Ronald Solomon Ohio State University, Columbus, OH
Softcover ISBN:  978-0-8218-0960-0
Product Code:  SURV/40.1.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $77.40
eBook ISBN:  978-1-4704-1267-8
Product Code:  SURV/40.1.S.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $75.00
Softcover ISBN:  978-0-8218-0960-0
eBook ISBN:  978-1-4704-1267-8
Product Code:  SURV/40.1.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $152.40 $114.90
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 401994; 165 pp
    MSC: Primary 20

    The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. Much of the book is written in an expository style accessible to nonspecialists.

    Readership

    The material here ranges from exposition suitable to a first- or second-year graduate student to more technical portions suitable for specialists.

  • Table of Contents
     
     
    • Part I
    • 1. Overview
    • 2. Outline of proof
  • Reviews
     
     
    • This new, second-generation proof is a great improvement while still being mostly based on the methods developed for the first proof... The entire organization of the proof is given in great detail. The wait for this project to reach this stage has been worth it.

      Mathematical Reviews
    • Written in extremely careful and clear style ... readable, and will repay those who work through it by giving them a detailed picture of the strategy of the whole proof.

      Bulletin of the London Mathematical Society
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 401994; 165 pp
MSC: Primary 20

The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This first volume, which sets up the structure for the entire series, begins with largely informal discussions of the relationship between the Classification Theorem and the general structure of finite groups, as well as the general strategy to be followed in the series and a comparison with the original proof. Also listed are background results from the literature that will be used in subsequent volumes. Next, the authors formally present the structure of the proof and the plan for the series of volumes in the form of two grids, giving the main case division of the proof as well as the principal milestones in the analysis of each case. Thumbnail sketches are given of the ten or so principal methods underlying the proof. Much of the book is written in an expository style accessible to nonspecialists.

Readership

The material here ranges from exposition suitable to a first- or second-year graduate student to more technical portions suitable for specialists.

  • Part I
  • 1. Overview
  • 2. Outline of proof
  • This new, second-generation proof is a great improvement while still being mostly based on the methods developed for the first proof... The entire organization of the proof is given in great detail. The wait for this project to reach this stage has been worth it.

    Mathematical Reviews
  • Written in extremely careful and clear style ... readable, and will repay those who work through it by giving them a detailed picture of the strategy of the whole proof.

    Bulletin of the London Mathematical Society
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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