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Applying the classification of finite simple groups : a user's guide /

Bibliographic Details
Main Author: Smith, Stephen D., 1948- (Author)
Format: Book
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2018]
Series:Mathematical surveys and monographs ; no. 230.
Subjects:
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.
Table of 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 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.