Indecomposable decompositions of torsion-free abelian groups

An indecomposable decomposition of a torsion-free abelian group G of rank n is a decomposition G = A(1) circle plus...circle plus A(t) where each A(t) is indecomposable of rank r(i), so that Sigma(i) r(i) = n is a partition of n. The group G may have indecomposable decompositions that result in different partitions of n. We address the problem of characterizing those sets of partitions of n which can arise from indecomposable decompositions of a torsion-free abelian group. (C) 2018 Elsevier Inc. All rights reserved.