Fully inert subgroups of torsion-complete p-groups

Abstract

The main result of this paper states that fully inert subgroups of torsion-complete abelian p-groups are commensurable with fully invariant subgroups, which have a satisfactory characterization by a classical result by Kaplansky. As the proof of this fact relies on the analogous result for direct sums of cyclic p-groups, we provide revisited and simplified proofs of the fact that fully inert subgroups of direct sums of cyclic p-groups are commensurable with fully invariant subgroups.