Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0997.20001
Aschbacher, Michael
Finite group theory. 2nd ed. (English)
[B] Cambridge Studies in Advanced Mathematics. 10. Cambridge: Cambridge University Press. xi, 304 p. \sterling 52.50; \$ 74.95 hbk; \sterling 19.95, \$ 32.95 pbk (2000). ISBN 0-521-78145-0/hbk; ISBN 0-521-78675-4/pbk

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.
[U.Dempwolff (Kaiserslautern)]

MSC 2000:: *20-02 Research monographs (group theory)
20Dxx Abstract finite groups
20-01 Textbooks (group theory)
20F05 Presentations of groups
20E08 Groups acting on trees
20F65 Geometric group theory
20C15 Ordinary representations and characters of groups
20B30 General theory of symmetric groups

Keywords: permutation representations; Sylow theorems; normal series; Jordan-Hölder theorem; characteristic subgroups; nilpotent groups; semidirect products; splitting group extensions; linear groups; permutation groups; Schur-Zassenhaus theorem; sesquilinear forms; isometry groups; $p$-groups; Coxeter groups; root systems; generalized Fitting group; signalizer functors; Thompson factorization; Schur multipliers; solvable groups; fusion; geometry of groups; Coxeter complexes; buildings; $(B,N)$-pairs; finite simple groups; involutions; Brauer-Fowler theorem; simple groups of Lie type; Thompson group; solvable 2-signalizer functor theorem

Citations: Zbl 0185.05701; Zbl 0463.20012; Zbl 0217.07201; Zbl 0514.20002; Zbl 0488.20002; Zbl 0477.20001; Zbl 0472.20001; Zbl 0412.20002; Zbl 0361.20001; Zbl 0826.20001; Zbl 0583.20001

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]