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On the Isomorphism of Some One-Relator Groups

A. V. Borschev·D. I. Moldavanskii
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Abstract

A class of one-relator groups such that every group in the class is determined by a triple of integers and is an HNN-extension of some Baumslag -- Solitar group is considered. A criterion for two groups in this class to be isomorphic and criterion for two non-isomorphic groups to be a homomorphic image of each other are obtained. This result leads to a negative answer to the question 3.33 from "Kourovka Notebook".

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A. V. Borschev, D. I. Moldavanskii. 2005-02-08. On the Isomorphism of Some One-Relator Groups. https://arxiv.org/abs/math/0502153

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