FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 3, PAGES 9-16

Normal subgroups of holomorphs of Abelian groups and almost holomorphic isomorphism

I. E. Grinshpon

Abstract

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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.

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Last modified: June 19, 2007