"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 second-year graduate course for students who have had first-year 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"--The publisher. Read more...
Abstract:
Since the 1980s, Classification of Finite Simple Groups (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. Read more...
Author(s): Smith, Stephen D
Series: Mathematical surveys and monographs no. 230
Publisher: American Mathematical Society
Year: 2018
Language: English
Pages: 231
Tags: Fi
Content: Background : simple groups and their properties --
Outline of the proof of the CFSG : some main ideas --
Thompson factorization --
and its failure : FF-methods --
Recognition theorems 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 A. Some supplementary notes to the text --
Appendix B. Further remarks on certain exercises.
