Theoretical analysis reveals an explicit non-Hopfian ascending HNN-extension of a finitely presented Hopfian group, indicating new structural boundaries analogous to the Sapir-Wise problem.
We discover the first example of 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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Kim et al. (2026) studied this question.
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