A representation theorem for abelian groups with no elements of infinite<i>p</i>-height

Abstract

The purpose of this note is to give a generalization of the representation Theorems 33.1 and 33.2 of [2], Let G be an arbitrary abelian group and B = [xei <#>] [ ^i Bi] be a p-basic subgroup of G, cf. [3], where e<#> is the torsionfree part. For all eA let (F*) be a copy of the group of p-adic integers, and let (F p ) denote the infinite cyclic group of finite p-adic integers in (F%)\. Then G can be mapped homomorphically into the complete direct sum[* e4 (F*)]0 [ki-B] with kernel p G. Furthermore, the image of G is a p-pure subgroup which contains [e^(F p ) ] [^i^] as a p-basic subgroup and is in turn contained in the p-adic completion of this subgroup (See Section 1 for definitions). This representation is completely analogous to the representation theorem for p-groups which is contained as a special case, and hopefully it is of similar use. Definitions and facts concerning p-adic and n-adic topologies*