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  3. Characters and Blocks of Finite Groups
  • Cited by 174
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
1998
Online ISBN:
9780511526015
DOI:
https://doi.org/10.1017/CBO9780511526015
Subjects:
Mathematics (general), Mathematics, Algebra
Series:
London Mathematical Society Lecture Note Series (250)
Information

Book 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.

Reviews

"features good organization, clear and detailed proofs, and good exercises...a strong pedagogical work and a worthy sequel to Isaacs' book on ordinary character theory." Bulletin of the AMS

"...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

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