Fully invariant subgroups of separable Abelian groups

The new description of fully invariant subgroups and their lattice for Abelian $p$-groups without elements of infinite height and large subgroups and their lattice for arbitrary Abelian $p$-groups is obtained. Ulm–Kaplansky invariants of these subgroups are calculated. The full description of fully invariant subgroups and their lattice for separable torsion free Abelian groups is obtained.