Characters and Blocks of Finite Groups

Gabriel Navarro

• Publisher: Cambridge University Press
• Year: 1998
• Print ISBN: 9780521595131
• eBook ISBN: 9780511893391
• Topic: Mathématiques
• Subtopic: Algèbre

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.

Table of contents

• Cover
• Half-title
• Tilte
• Copyright
• Dedication
• Contents
• Preface
• Chapter 1 Algebras
• Chapter 2 Brauer Characters
• Chapter 3 Blocks
• Chapter 4 The First Main Theorem
• Chapter 5 The Second Main Theorem
• Chapter 6 The Third Main Theorem
• Chapter 7 The Z*-Theorem
• Chapter 8 Brauer Characters as Characters
• Chapter 9 Blocks and Normal Subgroups
• Chapter 10 Characters and Blocks in p -Solvable Groups
• Chapter 11 Groups with Sylow p-Subgroups of Order p
• Notation
• Bibliographic notes
• References
• Index