Finite Group Theory

The book provides the basic foundations for the local theory of finite groups, the theory of classical linear groups, and the theory of buildings and BN-pairs.

M. Aschbacher (Author)

9780521781459, Cambridge University Press

Hardback, published 3 July 2000

320 pages, 25 b/w illus.
23.7 x 15.8 x 2.6 cm, 0.545 kg

'I consider this book as an extremely valuable source and help for anyone interested in a serious study of finite groups.' U. Dempwolff, Zentralblatt MATH

During the last 40 years the theory of finite groups has developed dramatically. The finite simple groups have been classified and are becoming better understood. Tools exist to reduce many questions about arbitrary finite groups to similar questions about simple groups. Since the classification there have been numerous applications of this theory in other branches of mathematics. Finite Group Theory develops the foundations of the theory of finite groups. It can serve as a text for a course on finite groups for students already exposed to a first course in algebra. It could supply the background necessary to begin reading journal articles in the field. For specialists it also provides a reference on the foundations of the subject. This second edition has been considerably improved with a completely rewritten Chapter 15 considering the 2-Signalizer Functor Theorem, and the addition of an appendix containing solutions to exercises.

1. Preliminary results
2. Permutation representations
3. Representations of groups on groups
4. Linear representations
5. Permutation groups
6. Extensions of groups and modules
7. Spaces with forms
8. p-Groups
9. Change of field of a linear representation
10. Presentations of groups
11. The generalized Fitting subgroup
12. Linear representations of finite groups
13. Transfer and fusion
14. The geometry of groups of Lie type
15. Signalizer functors
16. Finite simple groups.

Subject Areas: Algebra [PBF]