The lattice of fully invariant subgroups of a cotorsion hull (Q6150294)

Let \(A\) be an abelian group. A subgroup \(B \leq A\) is invariant if for any endomorphism of \(A\) it is mapped into itself. The group \(A\) is called a cotorsion group if its extension by any torsion-free group \(C\) splits, that is \(\mathrm{Ext}(C,A)=0\). In the paper under review, the author studies the lattices of fully invariant subgroups of cotorsion hulls for different classes of separable primary abelian groups. In particular, he considers the cases in which the primary group is a direct sum of cyclic \(p\)-groups, a direct sum of torsion-complete groups, or an additive group of the primary group of ring endomorphisms is a direct sum of a group of small endomorphisms and a \(p\)-adic completion of a direct sum of infinite cyclic groups.