Based on the results of generalized additions, multiplications and differences proven in Part I and II of this paper a framework for a general integral is presented. Moreover it is shown that many results of the literature are contained as special cases in our results.
In this article we study the problem of finding such finite groups that the modular forms associated with all elements of these groups by means of a certain faithful representation belong to a special class of modular forms (so-called multiplicative products). This problem is open.We find metacyclic groups with such property and describe the Sylow -subgroups, for such groups. We also give a review of the results about the connection between multiplicative -products and elements of finite orders...