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Finite group theory. 2nd ed. (English) Zbl 0997.20001
Cambridge Studies in Advanced Mathematics. 10. Cambridge: Cambridge University Press. xi, 304 p. £52.50; $ 74.95 hbk; £19.95, $ 32.95 pbk (2000).
In this second edition of Aschbacher’s monograph on finite groups a number of misprints of the first edition (1986; Zbl 0583.20001) have been removed. However, this new edition has two major improvements: Chapter 15 has been completely rewritten. It contains now a proof of the solvable 2-Signalizer Functor Theorem instead of the solvable Signalizer Functor Theorem of the first edition. In confining to the more special form of this theorem the proof has become considerably more transparent. The second major change is the addition of an appendix. In this extensive appendix carefully worked out solutions of selected exercises are presented. This should even more challenge the ambitious reader to tackle the demanding exercises of this book. In conclusion: this monograph has received some valuable improvements. This confirms the opinion of my first review: I consider this book as an extremely valuable source and help for anyone interested in a serious study of finite groups.
MSC:
20-02Research monographs (group theory)
20DxxAbstract finite groups
20-01Textbooks (group theory)
20F05Generators, relations, and presentations of groups
20E08Groups acting on trees
20F65Geometric group theory
20C15Ordinary representations and characters of groups
20B30General theory of symmetric groups