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Finite Groups
Daniel Gorenstein

AMS Chelsea Publishing
1968; 519 pp; hardcover
Volume: 301
ISBN-10: 0-8218-4342-7
ISBN-13: 978-0-8218-4342-0
List Price: US$68
Member Price: US$61.20
Order Code: CHEL/301.H
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See also:

Finite Group Theory - I Martin Isaacs

... it is required reading for anyone who wishes to study the subject.

--Mathematical Reviews

The theory of finite simple groups enjoyed a period of spectacular activity in the 1950s and 1960s. The first edition of Gorenstein's book was published in 1968, at the time of some of the first major classification results. The second edition was published in 1980, when it was clear that the classification was understood and the proof was within reach. Gorenstein's treatment of the subject proved prescient, as many of the developments between the two editions could be seen as continuations of the material in the book. Even now, the book remains one of the best sources for an introduction to finite groups and the classification of the simple groups. Gorenstein's insight provides a guiding light through the many pages that have been dedicated to the proof.


Undergraduates, graduate students, and research mathematicians interested in finite groups and the classification of the simple groups.

Table of Contents

Part I: Methods
  • Preliminaries
  • Some basic topics
  • Representations of groups
  • Character theory
  • Groups of prime power order
  • Solvable and \(\pi\)-solvable groups
  • Fusion, transfer, and \(p\)-factor groups
  • \(p\)-constrained and \(p\)-stable groups
  • Groups of even order
Part II: Applications
  • Fixed-point-free automorphisms
  • The Hall-Higman theorem
  • Groups with generalized quaternion Sylow 2-subgroups
  • Zassenhaus groups
  • Groups in which centralizers are nilpotent
  • Groups with self-centralizing Sylow 2-subgroups of order 4
Part III: General Classification Problems
  • Simple groups of low rank
  • The known simple groups
  • Bibliography
  • List of symbols
  • Index
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