Abelian Groups and Character Sums

Abstract

This first chapter should be viewed more as a reference chapter. The goal is to present several results concerning abelian groups that may have been missed in a standard first course in Group Theory. We begin first with basic notation used throughout the book, then some basic review leading up to the introduction of the concept of independent group elements, and conclude the chapter by developing the basics regarding characters of an abelian group. The latter will eventually give rise to the potent method of Character Sums, of which we will give two examples in later chapters.