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512.2 SMIT

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 Description
 xiii, 231 pages ; 27 cm.
 Notes
 Contents: Background : simple groups and their properties  Outline of the proof of the CFSG : some main ideas  Thompson factorization  and its failure : FFmethods  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.Includes bibliographical references and index.Summary: "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"  From the publisher.