Hardcover ISBN:  9781470442910 
Product Code:  SURV/230 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470446826 
Product Code:  SURV/230.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9781470442910 
eBook: ISBN:  9781470446826 
Product Code:  SURV/230.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 
Hardcover ISBN:  9781470442910 
Product Code:  SURV/230 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470446826 
Product Code:  SURV/230.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9781470442910 
eBook ISBN:  9781470446826 
Product Code:  SURV/230.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 230; 2018; 231 ppMSC: Primary 20
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG.
The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a secondyear graduate course for students who have had firstyear graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
ReadershipGraduate students and researchers interested in group theory and its applications.

Table of Contents

Chapters

Background: Simple groups and their properties

Outline of the proof of the CFSG: Some main ideas

Thompson factorization—and its failure: FFmethods

Recognition theorms for simple groups

Representation theory of simple groups

Maximal subgroups and primitive representations

Geometries for simple groups

Some fusion techniques for classification problems

Some applications close to finite group theory

Some applications farther afield from finite groups

Appendix

Appendix A. Some supplementary notes to the text

Appendix B. Further remarks on certain exercises


Additional Material

RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG.
The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a secondyear graduate course for students who have had firstyear graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
Graduate students and researchers interested in group theory and its applications.

Chapters

Background: Simple groups and their properties

Outline of the proof of the CFSG: Some main ideas

Thompson factorization—and its failure: FFmethods

Recognition theorms for simple groups

Representation theory of simple groups

Maximal subgroups and primitive representations

Geometries for simple groups

Some fusion techniques for classification problems

Some applications close to finite group theory

Some applications farther afield from finite groups

Appendix

Appendix A. Some supplementary notes to the text

Appendix B. Further remarks on certain exercises