With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.

No abstract

The first edition of the book (1993) was very well received, so that it was reprinted in 1995. This reviewer wrote the review on that (Zbl 0792.20006). Now in 2001, a second edition has been published. In comparison to the first edition, substantial additions have been made: In chapter 20 on Clifford's theorem on normal subgroups, in chapter 23 on the Brauer-Fowler theorem, in the former chapter 28 on remarks regarding Brauer's centralizer-of-an-involution techniques. Two new chapters have been added: chapter 28 on the character table of GL(2, p) and chapter 29 on permutations and characters.On the whole, this reviewer regards the second printing of the book as a gem in studying representation theory of finite groups.Reviewer: R.W.van der Waall (Amsterdam) MSC:20C15 Ordinary representations and characters 20-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory Cited in 113 Documents Keywords:ordinary representations; characters of groups; applications to molecular vibrations; introductory book; representation theory of finite groups; character calculations; groups of order p a q b ; GL(2, p); Clifford's theorem; Brauer-Fowler theorem; character tables

No abstract

No abstract