In the examination of the structure of certain classes of Abelian groups, the question arises, “Given a class of Abelian groups satisfying a certain structure theorem A, then is theorem A really applicable, or is theorem A so complicated and restricted that it is absolutely useless?" Kaplansky [1] proposed a list of three test problems for which he stated that, if theorem A can produce satisfactory results to these three test problems, then this might be a test of the usefulness of this class of Abelian groups. However, Walker [l], proved that test problem III, of Kaplansky, was true for all Abelian groups, and thus it cannot serve as a test for the usefulness of a certain theorem which applies only to a certain class of Abelian groups. It is the purpose of this thesis to generalize some of the main results of Walker's thesis, which lead up to the solution of Kaplansky's test problem III, to the more general case of a loop.