Fundamental Theorem for Finite Abelian Groups

In this chapter we state the Fundamental Theorem for Finite Abelian Groups, which completely describes the structure of such groups. This powerful theorem provides an easy-to-understand recipe by which all such groups can be constructed, using the two familiar notions of cyclic group and direct product. The theorem is relatively difficult to prove, and so we will not prove it here. The interested reader can refer to any introductory text in group theory. However, we will look more closely at a very special type of finite group called a p-group and prove a couple of important facts regarding them.