Representation Theory of Finite Groups: Algebra and Arithmetic
The book is an introduction to the group representation theory with emphasis on finite groups. Since group representations are just modules over group algebras, the classical results on semisimple group representations are naturally obtained in Chapter 3, as particular cases of more general results concerning the structure of modules over semisimple rings. The latter results are presented in Chapter 2. Chapter 4 deals with induced representations and culminates in the proof of Brauer's theorem (concerning irreducible complex representations of G of exponent n being defined over Q (n√1)). The remaining three chapters provide an introduction to modular representation theory, again by applying the powerful module theoretic approach. The book is well written, and contains many examples worked out in detail (for example, determining all irreducible complex and modular representations of A5). It is a suitable text for a year long graduate course on the subject.