Email this article The Isomorphism Problem for Generalized Baumslag–Solitar Groups with One Mobile Edge
- Authors: Dudkin F.A.1,2
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 56, No 3 (2017)
- Pages: 197-209
- Section: Article
- URL: https://journal-vniispk.ru/0002-5232/article/view/234035
- DOI: https://doi.org/10.1007/s10469-017-9440-y
- ID: 234035
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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(????) of some labeled graph ????. This paper deals with the isomorphism problem for GBS groups, which is the problem of determining whether π1(????) ≅ π1(????) for two given labeled graphs ???? and ????. We describe an algorithm that decides this problem for the case where one of the labeled graphs has a sole mobile edge.
About the authors
F. A. Dudkin
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: DudkinF@ngs.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 1, Novosibirsk, 630090
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