Geodesic
Admissible slides for generalized Baumslag--Solitar groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 552-561

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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. Any $GBS$ group is isomorphic to fundamental group $\pi_1(\mathbb{A})$ of some labeled graph $\mathbb{A}$. Slide is a transformation of labeled graphs. Slides play an important role in isomorphism problem for GBS groups. Given an edge $e$ with label $\lambda$ and $\alpha\in\mathbb{Q}$. In this paper we describe an algorithm that checks if there exists a cycle $p$ such that after slide $e$ over $p$ label $\lambda$ multiplies by $\alpha$ or not. If such cycle exists then the algorithm finds one of them.
Keywords: isomorphism problem, generalized Baumslag–Solitar group, labeled graph. 
@article{SEMR_2015_12_a19,
     author = {F. A. Dudkin},
     title = {Admissible slides for generalized {Baumslag--Solitar} groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {552--561},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a19/}
}
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F. A. Dudkin. Admissible slides for generalized Baumslag--Solitar groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 552-561. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a19/