Completely torsion-free, finite-rank, almost decomposable groups with torsion factor

This paper deals with almost completely decomposable finite-rank groups G that have rank-1 summands of pairwise noncomparable types. It is well known that every such group has a unique complete quasi-decomposition A with respect to equality. We consider the number of almost completely decomposable groups G with a given quasi-decomposition A for which G/A is isomorphic to ℤ(p m). © 2008 Springer Science+Business Media, Inc.