A recipe for constructing non-Hopfian relatively hyperbolic groups with Hopfian peripheral subgroups

Jan Kim; Tattybubu Arap kyzy; Donghi Lee

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arXiv · 2306.14215

A recipe for constructing non-Hopfian relatively hyperbolic groups with Hopfian peripheral subgroups

Jan Kim·Tattybubu Arap kyzy·Donghi Lee

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Abstract

Very recently, Kim and Lee presented an example of a non-Hopfian relatively hyperbolic group with a Hopfian peripheral subgroup, demonstrating a counterexample to Osin's well-known question (Problem 5.5). In this paper, we provide a general construction method using the so-called image extension theorem to generate non-Hopfian relatively hyperbolic groups with Hopfian peripheral subgroups. Additionally, we provide two specific examples using this construction method.

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BibTeX RIS

Jan Kim, Tattybubu Arap kyzy, Donghi Lee. 2023-06-25. A recipe for constructing non-Hopfian relatively hyperbolic groups with Hopfian peripheral subgroups. https://arxiv.org/abs/2306.14215

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