Representation Theory of Finite Groups

This volume contains a concise exposition of the theory of finite groups, including the theory of modular representations. The rudiments of linear algebra and knowledge of the elementary concepts of group theory are useful, if not entirely indispensable, prerequisites for reading this book; most of the other requisites, such as the theory of p-adic fields, are developed in the text. After an introductory chapter on group characters, repression modules, applications of ideas and results from group theory and the regular representation, the author offers penetrating discussions of the representation theory of rings with identity, the representation theory of finite groups, applications of the theory of characters, construction of irreducible representations and modular representations. Well-chosen exercises are included throughout to help students test their understanding of the material. An appendix on groups, rings, ideals, and fields, as well as a bibliography, round out this useful well-thought-out text. Graduate students wishing to acquire some knowledge of representation theory will find this an excellent text for self-study. The book also lends itself to use as supplementary reading for a course in group theory or in the applications of representation theory to physics.