ABSTRACT
W e just discussed some basic concepts of modern algebra inChapter 7. With these preliminaries, we are able to introduce an algebraic system with one algebraic operation-the group. Group theory is an important topic of study in modern algebra. It has a great application in cryptography, especially in public key cryptography. In this chapter, the concepts and related properties of groups, cyclic groups and subgroups, will be given. We will also introduce an important tool in the study of groups-the fundamental homomorphism theorem.
