K0-like constructions for almost completely decomposable groups

Abstract

In an earlier paper the authors introduced a K 0 -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 K 0 construction for acd groups, one always obtains a trivial torsion subgroup. Thus, G ( A ) appears to be a more versatile tool than K 0 for the study of acd's.