On Some Versions of Hopficity for Abelian Groups

Peter V. Danchev; Patrick W. Keef

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arXiv · 2512.21223

On Some Versions of Hopficity for Abelian Groups

Peter V. Danchev·Patrick W. Keef

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Abstract

We completely 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.

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Peter V. Danchev, Patrick W. Keef. 2025-12-24. On Some Versions of Hopficity for Abelian Groups. https://arxiv.org/abs/2512.21223

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