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Full Description
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.
Contents
Background: Simple groups and their properties
Outline of the proof of the CFSG: Some main ideas
Thompson factorization--and its failure: FF-methods
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 A: Some supplementary notes to the text
Appendix B: Further remarks on certain exercises
Bibliography
Index.
