Torsion abelian $afi$-groups

A subgroup $A$ of an abelian group $G$ is called its absolute ideal if $A$ is an ideal of any ring on $G$. An abelian group is called an $afi$-group if every its absolute ideal is a fully invariant subgroup. In this paper descriptions of afi-groups in the class of fully-transitive torsion groups (particularly, separable torsion groups) and divisible torsion groups are given.