Work

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

Year: 2026

Type: article

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.

Source: International Journal of Algebra and Computation

DOI: 10.1142/s0218196726500530

Authors: Jan Kim, Junseok Kim, Yoonjin Lee

Institutions: Ewha Womans University, Technion – Israel Institute of Technology

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, National Research Foundation of Korea

Awards: G3147530241, G3308718102, G3793286438, G6312077453, G7891000231