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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 2012, Volume 17, Issue 8, Pages 35–46 (Mi fpm1469)

Determinateness of torsion-free Abelian groups by their holomorphs and almost holomorphic isomorphism

S. Ya. Grinshpona, I. E. Grinshponb

a Tomsk State University
b Tomsk State University of Control Systems and Radioelectronics

Abstract: In this paper, we study holomorphically isomorphic Abelian groups, i.e., Abelian groups with isomorphic holomorphs. We also study a generalization of the concept of holomorphic isomorphism, namely, almost holomorphic isomorphism, which is deeply connected with normal Abelian subgroups of holomorphs of Abelian groups. Torsion-free Abelian groups that are determined by their holomorphs are highlighted from different classes. In particular, it has been found that any homogeneous separable group can be determined by its holomorph in the class of all Abelian groups.

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English version:
Journal of Mathematical Sciences (New York), 2014, 197:5, 605–613

UDC: 512.541

Citation: S. Ya. Grinshpon, I. E. Grinshpon, “Determinateness of torsion-free Abelian groups by their holomorphs and almost holomorphic isomorphism”, Fundam. Prikl. Mat., 17:8 (2012), 35–46; J. Math. Sci., 197:5 (2014), 605–613

Citation in format AMSBIB
\Bibitem{GriGri12} \by S.~Ya.~Grinshpon, I.~E.~Grinshpon \paper Determinateness of torsion-free Abelian groups by their holomorphs and almost holomorphic isomorphism \jour Fundam. Prikl. Mat. \yr 2012 \vol 17 \issue 8 \pages 35--46 \mathnet{http://mi.mathnet.ru/fpm1469} \transl \jour J. Math. Sci. \yr 2014 \vol 197 \issue 5 \pages 605--613 \crossref{https://doi.org/10.1007/s10958-014-1742-1} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84893856642}