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Softcover ISBN:  9780821809600 
Product Code:  SURV/40.1.S 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $77.40 
eBook ISBN:  9781470412678 
Product Code:  SURV/40.1.S.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $75.00 
Softcover ISBN:  9780821809600 
eBook ISBN:  9781470412678 
Product Code:  SURV/40.1.S.B 
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MAA Member Price:  $228.60 $172.35 
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Book DetailsMathematical Surveys and MonographsVolume: 40; 1994; 165 ppMSC: 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.
ReadershipThe material here ranges from exposition suitable to a first or secondyear graduate student to more technical portions suitable for specialists.

Table of Contents

Part I

1. Overview

2. Outline of proof


Reviews

This new, secondgeneration 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


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

Part I

1. Overview

2. Outline of proof

This new, secondgeneration 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