Introduction -- Background Material -- Solvable Linear Groups and Gluck’s Permutation Lemma -- Gluck’s Conjecture -- The Huppert ρ-σ Conjecture -- Dolfi’s Theorem -- Induction and Restriction of Characters From p-Complements -- Brauer Graphs of Solvable Groups, I -- Brauer Graphs of Solvable Groups, II -- Conjugacy Classes, Codegrees, Zeros, and other Applications.

This book highlights recent developments in the representation theory of finite solvable groups, which seeks to connect group theory to linear algebra in ways that allow for better study of the groups in question. Over the last several decades, a number of results in the representations of solvable groups have been proven using so-called “large orbit” theorems. This book provides an extensive survey of the current state of the large-orbit theorems. The authors outline the proofs of the large orbit theorems to provide an overview of the topic, then demonstrate how these theorems can be used to prove new results about solvable groups. In addition, this book: Discusses recent developments in the representation theory of finite solvable groups Provides an extensive survey of the current state of the large-orbit theorems, providing a broad overview of the topic Includes proofs that demonstrate how these theorems can be applied to prove new results about solvable groups.