Characters and Blocks of Finite Groups

Research text on algebra/representation theory.

Gabriel Navarro (Author)

9780521595131, Cambridge University Press

Paperback, published 7 May 1998

300 pages
22.9 x 15.2 x 1.7 cm, 0.413 kg

"...a wealth of deep and interesting results which cannot be found in other textbooks...The book is very well written...it contains many jewels otherwise spread throughout the literature." Mathematical Reviews

This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Finally, the character theory of groups with a Sylow p-subgroup of order p is studied. Each chapter concludes with a set of problems. The book is aimed at graduate students, with some previous knowledge of ordinary character theory, and researchers studying the representation theory of finite groups.

Preface
1. Algebras
2. Brauer characters
3. Blocks
4. The first main theorem
5. The second main theorem
6. The third main theorem
7. The Z*-theorem
8. Brauer characters as characters
9. Blocks and normal subgroups
10. Characters and blocks in p-solvable groups
11. Groups with Sylow p-subgroups of order p
Notation
Bibliographic notes
References
Index.

Subject Areas: Algebra [PBF]