Abstract
We consider the problem of full transitivity of the cotorsion hull 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
is fully transitive if and only if T is the direct sum of the cyclic p-groups or a torsion-complete group.
Acknowledgments
I would like to thank the reviewers for careful review they made of the paper and their comments that improved the content of the original text. I also want to describe the respect I have for Dr. Mandi Schaeffer Fry, Associate Editor, for her professional editorial management of the present submission.