On the Similarity of Almost Holomorphically Isomorphic Direct Products of Torsion Free Groups

Two groups are said to be almost holomorphically isomorphic if each of them is isomorphic to a normal subgroup of the holomorph of the other group. The similarity of almost holomorphically isomorphic direct products of torsion free abelian groups from some class is studied. Besides the problem of determinateness of a group by its holomorph is considered.