Finite Group Theory

ISBN-13: 9780521786751 / Angielski / Miękka / 2000 / 318 str.

M. Aschbacher; Michael Aschbacher; B. Bollobas

Opis

This second edition develops the foundations of finite group theory. For students already exposed to a first course in algebra, it serves as a text for a course on finite groups. For the reader with some mathematical sophistication but limited knowledge of finite group theory, the book supplies the basic background necessary to begin to read journal articles in the field. It also provides the specialist in finite group theory with a reference on the foundations of the subject. Unifying themes include the Classification Theorem and the classical linear groups. Lie theory appears in chapters on Coxeter groups, root systems, buildings, and Tits systems. 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.

Recenzje

'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

Spis treści

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.