Representations and Characters of Groups, Second Edition

1

Groups and homomorphisms

This book is devoted to the study of an aspect of group theory, so we begin with a résumé of facts about groups, most of which you should know already. In addition, we introduce several examples, such as dihedral groups and symmetric groups, which we shall use extensively to illustrate the later theory. An elementary course on abstract algebra would normally cover all the material in the chapter, and any book on basic group theory will supply you with further details. One or two results which we shall use only infrequently are demoted to the exercises at the end of the chapter – you can refer to the solutions if necessary.

Groups

A group consists of a set G, together with a rule for combining any two elements g, h