Rudiments of Group Theory

Abstract

In this introductory chapter, we review the elementary notions of group theory and develop many of the tools that we will use in the remaining chapters. Section 1 consists primarily of those facts with which we assume the reader is familiar from some prior study of group theory; consequently, most proofs in this section have been omitted. In Section 2 we introduce some important concepts, such as automorphism groups and semidirect products, which are not necessarily covered in a first course on group theory. Section 3 treats the theory of group actions; here we present both elementary applications and results of a more technical nature which will be needed in later chapters.