Some properties of FC-groups which occur as automorphism groups

Abstract:

We prove that if $G$ is a group such that Aut $G$ is a countably infinite torsion $FC$-group, then Aut $G$ contains an infinite locally soluble, normal subgroup and hence a nontrivial abelian normal subgroup. It follows that a countably infinite subdirect product of nontrivial finite groups, of which only finitely many have nontrivial abelian normal subgroups, is not the automorphism group of any group.