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Determinateness of Torsion-Free Abelian Groups by Their Holomorphs and Almost Holomorphic Isomorphism

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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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Authors and Affiliations

  1. Tomsk State University, Tomsk, Russia

    S. Ya. Grinshpon

  2. Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia

    I. E. Grinshpon

Authors
  1. S. Ya. Grinshpon
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  2. I. E. Grinshpon
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Correspondence to S. Ya. Grinshpon.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 8, pp. 35–46, 2011/12.

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Grinshpon, S.Y., Grinshpon, I.E. Determinateness of Torsion-Free Abelian Groups by Their Holomorphs and Almost Holomorphic Isomorphism. J Math Sci 197, 605–613 (2014). https://doi.org/10.1007/s10958-014-1742-1

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  • DOI: https://doi.org/10.1007/s10958-014-1742-1

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