A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group
arXiv:2512.09135
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.
9 pages, Comments are welcome! v2: we update the authors' information and slightly change Introduction and Acknowledgement