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<p>We describe in certain important cases the class of commutative <i>co-finitely Hopfian</i> groups as defined by Bridson-Groves-Hillman-Martin in the journal Groups, Geometry, and Dynamics on 2010 (see [<CitationRef CitationID="CR3">3</CitationRef>]). We also consider and give a satisfactory description of several related classes of commutative groups. We also discuss in the commutative case a slightly more general version of co-finitely Hopfian groups called <i>almost co-finitely Hopfian</i> groups, as well as a more general version of Hopfian groups called <i>almost finitely Hopfian</i> groups.</p>

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On Some Versions of Hopficity for Abelian Groups

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Peter V. Danchev,
  • Patrick W. Keef

摘要

We describe in certain important cases the class of commutative co-finitely Hopfian groups as defined by Bridson-Groves-Hillman-Martin in the journal Groups, Geometry, and Dynamics on 2010 (see [3]). We also consider and give a satisfactory description of several related classes of commutative groups. We also discuss in the commutative case a slightly more general version of co-finitely Hopfian groups called almost co-finitely Hopfian groups, as well as a more general version of Hopfian groups called almost finitely Hopfian groups.