The lattice of fully invariant subgroups of a cotorsion hull

We consider lattices of fully invariant subgroups of cotorsion hulls for various classes of separable primary abelian groups. Based on the results of A. Mader, A. I. Moskalenko, A. L. S. Corner, and R. S. Pierce, we examine these lattices in situations where the primary group is the direct sum of cyclic $p$-groups, the direct sum of torsion-complete groups, or an additive group of the primary group of ring endomorphisms is the direct sum of a group of small endomorphisms and a $p$-adic completion of the direct sum of infinite cyclic groups. The questions concerning the full transitivity of a cotorsion hull are discussed.