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arXiv · 2512.09135

A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group

Jan Kim·Junseok Kim·Yoonjin Lee
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Abstract

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.

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Jan Kim, Junseok Kim, Yoonjin Lee. 2025-12-09. A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group. https://arxiv.org/abs/2512.09135

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