Normal subgroups of holomorphs of Abelian groups and almost holomorphic isomorphism

Abstract

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. In this paper, we study normal subgroups of holomorphs of Abelian groups and highlight some torsion-free groups for which almost holomorphic isomorphism implies isomorphism. In addition, we consider the problem of determinateness of a group by its holomorph.