"The purpose of this paper is to present a detailed account of the main aspects of the theory of direct products of groups with operators which satisfy the descending and ascending chain conditions for normal operator subgroups. The final objective is the well known Krull-Schmidt Theorem on the uniqueness of the direct product decomposition"--Introduction. / Typescript. / "June, 1987." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Nickolas Heerema, Professor Directing Paper. / Includes bibliographical references (leaf 27).

The main purpose of this thesis is to describe methods of constructing computer-free proofs of existence of finite groups and give useful techniques to perform double coset enumeration of groups with symmetric presentations over their control groups.