Applying the classification of finite simple groups : a user's guide
 Responsibility
 Stephen D. Smith.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2018]
 Copyright notice
 ©2018
 Physical description
 xiii, 231 pages ; 27 cm.
 Series
 Mathematical surveys and monographs ; no. 230.
Access
Available online
Science Library (Li and Ma)
Stacks
Call number  Status 

QA3 .A4 V.230  Unknown 
More options
Creators/Contributors
 Author/Creator
 Smith, Stephen D., 1948 author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 199211) and index.
 Contents

 Background: Simple groups and their properties Outline of the proof of the CFSG: Some main ideas Thompson factorizationand 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 A: Some supplementary notes to the text Appendix B: Further remarks on certain exercises Bibliography Index.
 (source: Nielsen Book Data)9781470442910 20180514
 Publisher's 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.
(source: Nielsen Book Data)9781470442910 20180514
Subjects
 Subject
 Finite simple groups.
 Representations of groups.
 Group theory and generalizations  Research exposition (monographs, survey articles)
 Group theory and generalizations  Abstract finite groups  Finite simple groups and their classification.
 Group theory and generalizations  Permutation groups  Permutation groups.
 Group theory and generalizations  Representation theory of groups  Representation theory of groups.
 Group theory and generalizations  Structure and classification of infinite or finite groups  Structure and classification of infinite or finite groups.
 Group theory and generalizations  Linear algebraic groups and related topics  Linear algebraic groups and related topics.
 Group theory and generalizations  Connections with homological algebra and category theory  Connections with homological algebra and category theory.
 Finite simple groups.
 Representations of groups.
 Group theory and generalizations  Research exposition (monographs, survey articles)
 Group theory and generalizations  Abstract finite groups  Finite simple groups and their classification.
 Group theory and generalizations  Permutation groups  Permutation groups.
 Group theory and generalizations  Representation theory of groups  Representation theory of groups.
 Group theory and generalizations  Structure and classification of infinite or finite groups  Structure and classification of infinite or finite groups.
 Group theory and generalizations  Linear algebraic groups and related topics  Linear algebraic groups and related topics.
 Group theory and generalizations  Connections with homological algebra and category theory  Connections with homological algebra and category theory.
 Finite simple groups.
 Representations of groups.
Bibliographic information
 Publication date
 2018
 Copyright date
 2018
 Title Variation
 Classification of finite simple groups
 Series
 Mathematical surveys and monographs ; volume 230
 ISBN
 9781470442910 hardcover
 1470442914 hardcover