Completely Torsion-free, Finite-rank, Almost Decomposable Groups With Torsion Factor

摘要

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).