AMS Chelsea Publishing 1968; 519 pp; hardcover Volume: 301 ISBN10: 0821843427 ISBN13: 9780821843420 List Price: US$68 Member Price: US$61.20 Order Code: CHEL/301.H
 ... 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. Readership 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  Fixedpointfree automorphisms
 The HallHigman theorem
 Groups with generalized quaternion Sylow 2subgroups
 Zassenhaus groups
 Groups in which centralizers are nilpotent
 Groups with selfcentralizing Sylow 2subgroups of order 4
Part III: General Classification Problems  Simple groups of low rank
 The known simple groups
 Bibliography
 List of symbols
 Index
