MATHEMATICS

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

I. È. Grinshpon

Tomsk State University of Control Systems and Radioelectronics

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. 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.

Keywords: torsion free abelian group, holomorph, direct product, similarity of groups, transitive group, homogeneous group, rank.

UDC: 512.541


Accepted: May 29, 2008