On products of primary abelian groups

Abstract

The t-product of a family { G i } iϵI of abelian p-groups is the torsion subgroup of Π iϵI G i , which we denote by Π iϵI t G i . The t-product is, in the homological sense, the direct product in the category of abelian p-groups. Since the usual way of writing a torsion-complete group is as a t-product, the notion of t-product provides a way of generalizing this important class of groups. Various properties of t-products are proven. An important part of the study of direct products is the consideration of their epimorphic images. This is also the case with t-products, where we are able to obtain analogous results. Of particular interest are those epimorphic images which are direct sums of cyclics. Applications are given to the ⊕ c -topology. As is frequently the case with homomorphisms defined on products, the index sets will be assumed to be non-measurable.