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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 = [φxei ] θ [φ ^i Bi] be a p-basic subgroup of G, cf. [3], where ®λeΛ is the torsionfree part. For all λeA let (F*)λ be a copy of the group of p-adic integers, and let (Fp)χ denote the infinite cyclic group of finite p-adic integers in (F%)\. Then G can be mapped homomorphically into the complete direct sum[Φ* e4 (F*)λ]0 [φΐki-Bΐ] with kernel pωG. Furthermore, the image of G is a p-pure subgroup which contains [φλe^(Fp)λ] φ [Φ^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.

A representation theorem for abelian groups with no elements of infinitep-height