This article is cited in 6 papers

The isomorphism problem for generalized Baumslag–Solitar groups with one mobile edge

F. A. Dudkin<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
^b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: A generalized Baumslag–Solitar group ($GBS$ group) is a finitely generated group $G$ which acts on a tree with all edge and vertex stabilizers infinite cyclic. Every $GBS$ group is the fundamental group $\pi_1(\mathbb A)$ of some graph labeled $\mathbb A$. This paper deals with the isomorphism problem for $GBS$ groups, which is the problem of determining whether $\pi_1(\mathbb A)\cong\pi_1(\mathbb B)$ for two given graphs labeled $\mathbb A$ and $\mathbb B$. We describe an algorithm that decides this problem for the case where one of the labeled graphs has one mobile edge.

Keywords: isomorphism problem, generalized Baumslag–Solitar group, labeled graph.

UDC: 512.54

Received: 04.02.2016

DOI: 10.17377/alglog.2017.56.302

 English version: Algebra and Logic, 2017, 56:3, 197–209

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