Representation type of finite rank almost completely decomposable groups

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