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An almost completely decomposable (acd) group is afiniterank torsion-free abelian group containing a finite direct sum of rank-1 groups as a subgroup of finite index. This paper is devoted to a determination of the representation type of indecomposables in categories of acd groups. In the process, representation types of categories of related representations of finite partially ordered sets (posets) over the rings  Z/p j Z  and  Z p  , the localization of the integers  Z  at a prime  p , are also determined.

Representation type of finite rank almost completely decomposable groups