A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group
Abstract
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Advanced Operator Algebra Research
Publication details
- Journal / source
- International Journal of Algebra and Computation
- Publisher
- World Scientific Pub Co Pte Ltd
- Pages
- 1–9
- Publication date
- 11 September 2026
- Language
- EN