On Strongly Hopfian Mixed Abelian Groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911727345467392 |
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| author | Danchev, Peter V. Keef, Patrick W. |
| author_facet | Danchev, Peter V. Keef, Patrick W. |
| contents | The classes of abelian groups that are (uniformly) strongly Hopfian abelian groups, and dually, (uniformly) strongly co-Hopfian abelian groups have been studied by several authors, including Abdelalim (2015) and Abdelalim-Chillali-Essanouni (2015). This paper extends these investivations in the case of (genuinely) mixed groups. For example, it is shown that a reduced group that is (uniformly) strongly co-Hopfian will always be (uniformly) strongly Hopfian. In addition, a result of Chekhlov-Danchev (submitted) characterizing when a torsion-free group is (uniformly) strongly Hopfian is generalized to the case of (global) Warfield groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29735 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Strongly Hopfian Mixed Abelian Groups Danchev, Peter V. Keef, Patrick W. Group Theory 20K10, 20K20, 20K21, 20K30 The classes of abelian groups that are (uniformly) strongly Hopfian abelian groups, and dually, (uniformly) strongly co-Hopfian abelian groups have been studied by several authors, including Abdelalim (2015) and Abdelalim-Chillali-Essanouni (2015). This paper extends these investivations in the case of (genuinely) mixed groups. For example, it is shown that a reduced group that is (uniformly) strongly co-Hopfian will always be (uniformly) strongly Hopfian. In addition, a result of Chekhlov-Danchev (submitted) characterizing when a torsion-free group is (uniformly) strongly Hopfian is generalized to the case of (global) Warfield groups. |
| title | On Strongly Hopfian Mixed Abelian Groups |
| topic | Group Theory 20K10, 20K20, 20K21, 20K30 |
| url | https://arxiv.org/abs/2605.29735 |