On the full transitivity of a cotorsion hull of a separable primary abelian group

Abstract

We consider the problem of full transitivity of the cotorsion hull T • of a separable primary group T, which is important in describing the lattice of fully invariant subgroups of a group. It is proved that the hull T • is fully transitive if and only if T is the direct sum of the cyclic p-groups or a torsion-complete group.