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On Infinite Groups with Given Properties of the Norm of Infinite Subgroups

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Ukrainian Mathematical Journal Aims and scope

Abstract

We investigate the relationship between the norm N G(∞) of infinite subgroups of an infinite group G and the structure of this group. We prove that N G(∞) is Abelian in the nonperiodic case, and a locally finite group is a finite extension of a quasicyclic subgroup if N G(∞) is a non-Dedekind group. In both cases, we describe the structure of the group G under the condition that the subgroup N G(∞) has finite index in G.

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Authors and Affiliations

  1. Sumy Pedagogic University, Sumy

    F. M. Liman & T. D. Lukashova

Authors
  1. F. M. Liman
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  2. T. D. Lukashova
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Liman, F.M., Lukashova, T.D. On Infinite Groups with Given Properties of the Norm of Infinite Subgroups. Ukrainian Mathematical Journal 53, 719–725 (2001). https://doi.org/10.1023/A:1012526216221

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  • DOI: https://doi.org/10.1023/A:1012526216221

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