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Applying the Classification of Finite Simple Groups: A User's Guide

Applying the Classification of Finite Simple Groups: A User's Guide

Autorzy
Wydawnictwo American Mathematical Society
Data wydania 01/02/2018
Liczba stron 231
Forma publikacji książka w twardej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
Język angielski
ISBN 9781470442910
Kategorie Algebra
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Opis książki

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.

Applying the Classification of Finite Simple Groups: A User's Guide

Spis treści

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.

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