Cyclic subgroup transitivity for Abelian groups

Abstract

In previous work, the first two authors studied the notion of transitivity with respect to cyclic subgroups for separable Abelian $p$-groups and modules over the ring of $p$-adic integers. Here we consider briefly how the notion can be used in the context of torsion-free Abelian groups and also look at the situation for non-separable $p$-groups and direct sums of infinite-rank homocyclic $p$-groups.