Character Theory of Finite Groups (Google eBook)

Front Cover
American Mathematical Soc., 1976 - Mathematics - 303 pages
2 Reviews
Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group. The book begins by developing the module theory of complex group algebras. After the module-theoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging. In addition to the development of the basic theory (using a cleaner notation than previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters. This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory, appearing in the bibliography of almost every research paper in the subject. It is largely self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.
  

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Contents

Group representations and characters
13
Characters and integrality
33
Products of characters
47
Induced characters
62
Normal subgroups
78
T I sets and exceptional characters
99
Brauers theorem
126
Changing the field
144
The Schur index
160
Projective representations
174
Character degrees
198
Character correspondence
219
Linear groups
240
Changing the characteristic
262
Appendix Some character tables
287
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