Character theory of finite groups

Representation theory and character theory are basic tools for the study of the structure of finite groups. Based on the classical results by Frobenius, Burnside, and Schur, character theory makes a central contribution to the complete classification of finite simple groups. This book serves as a modern introduction to this important part of group theory.

The book gives in its first section a self-contained introduction to the character theory of finite groups, which can be used for a first lecture on the subject. Later sections concentrate on Clifford theory, that is the relations between characters of a group and its normal subgroups.

This theory has many applications for solvable groups. Character degrees and lengths of conjugacy classes are studied in detail. Isaacs’s theory of p-special characters is included with several applications. The text contains many recent results that are not published in previous books on the same subject.