A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918240825901056 |
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| author | Kim, Jan Kim, Junseok Lee, Yoonjin |
| author_facet | Kim, Jan Kim, Junseok Lee, Yoonjin |
| contents | We find a non-Hopfian ascending HNN-extension of a finitely presented Hopfian group by providing an explicit construction. This result addresses an analogous question to the one posed by Sapir and Wise, which asks whether there is a non-residually finite ascending HNN-extension of a finitely presented residually finite group. Such an analogy is motivated by Mal'cev's result that every finitely generated residually finite group is Hopfian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group Kim, Jan Kim, Junseok Lee, Yoonjin Group Theory 20E06, 20E26, 20F67 We find a non-Hopfian ascending HNN-extension of a finitely presented Hopfian group by providing an explicit construction. This result addresses an analogous question to the one posed by Sapir and Wise, which asks whether there is a non-residually finite ascending HNN-extension of a finitely presented residually finite group. Such an analogy is motivated by Mal'cev's result that every finitely generated residually finite group is Hopfian. |
| title | A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group |
| topic | Group Theory 20E06, 20E26, 20F67 |
| url | https://arxiv.org/abs/2512.09135 |