This article is cited in 5 papers

Normal subgroups of holomorphs of Abelian groups and almost holomorphic isomorphism

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. 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.

UDC: 512.541

Received: 01.05.2006

 English version: Journal of Mathematical Sciences (New York), 2008, 154:3, 284–289

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