K0-like constructions for almost completely decomposable groups

In an earlier paper the authors introduced a K0-like construction that produces, for each torsion-free abelian group A of finite rank, a finitely generated abelian group G(A). In this note, we show that for any finite abelian group S, there is an almost completely decomposable (acd) group A such that G(A) has torsion subgroup isomorphic to S. In addition, if S is a finitely generated abelian group satisfying a certain condition on the torsion-free rank, then there is an almost completely decomposable group A such that G(A) S. In the usual K0 construction for acd groups, one always obtains a trivial torsion subgroup. Thus, G(A) appears to be a more versatile tool than K0 for the study of acdʹs.