The Isomorphism Problem for Generalized Baumslag–Solitar Groups with One Mobile Edge

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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 π1(A) of some labeled graph A. This paper deals with the isomorphism problem for GBS groups, which is the problem of determining whether π1(A) ≅ π1(A) for two given labeled graphsA and B. We describe an algorithm that decides this problem for the case where one of the labeled graphs has a sole mobile edge.

Original languageEnglish
Pages (from-to)197-209
Number of pages13
JournalAlgebra and Logic
Volume56
Issue number3
DOIs
Publication statusPublished - 1 Jul 2017

Keywords

  • generalized Baumslag–Solitar group
  • isomorphism problem
  • labeled graph
  • TREES
  • generalized Baumslag-Solitar group

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