Representations of Solvable Groups [Paperback]

In this book Manz and Wolf concentrate on that part of representation theory which relates to solvable groups.The role of representation theory in algebra is an important one. This volume concentrates on that part of the theory which relates to solvable groups. In particular, modules over finite fields are studied, but some applications to ordinary and Brauer characters of solvable groups are also given.The role of representation theory in algebra is an important one. This volume concentrates on that part of the theory which relates to solvable groups. In particular, modules over finite fields are studied, but some applications to ordinary and Brauer characters of solvable groups are also given.The role of representation theory in algebra is an important one and in this book Manz and Wolf concentrate on that part of the theory that relates to solvable groups. In particular, modules over finite fields are studied, but also some applications to ordinary and Brauer characters of solvable groups are given. The authors include a proof of Brauer's height-zero conjecture and a new proof of Huppert's classification of 2-transitive solvable permutation groups.Preliminaries; 1. Solvable subgroups of linear groups; 2. Solvable permutation groups; 3. Module actions with large centralizers; 4. Prime power divisors of character degrees; 5. Complexity of character degrees; 6. p-special characters. This is a very readable and coherent expository monograph, aimed at mathematicians and advanced students who desire a thorough knowledge of some of the main topics in the representation theory of finite solvable groups. The book features complete proofs and extensive background material. David Gluck, Mathematical Reviews