6533b858fe1ef96bd12b6c4c

RESEARCH PRODUCT

Characters and Blocks of Finite Groups

Gabriel Navarro

subject

AlgebraNormal subgroupPure mathematicsModular representation theoryBrauer's theorem on induced charactersSylow theoremsCharacter theoryOrder (group theory)Classification of finite simple groupsRepresentation theory of finite groupsMathematics

description

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.

yearjournalcountryeditionlanguage
1998-05-07
https://doi.org/10.1017/cbo9780511526015