1. We consider the following question posed by E. Weinberg [4, ?5.2]: Does there exist a torsion-free abelian group of cardinality greater than the continuum (K) with the property that each pure subgroup is (directly) indecomposable? In ?2 we answer this question negatively for a large class of groups which contains, most notably, the class of homogeneous groups. In ?3 we characterize, in terms of indecomposability, the pure and p-pure subgroups of the p-adic integers. Throughout this note all groups are abelian. The notation follows the usage in [2].