Geodesic
Computation of the centralizer dimension of generalized Baumslag–Solitar groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1823-1841

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A finitely generated group $G$ acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag-Solitar group ($GBS$ group). The centralizer dimension of a group $G$ is the maximal length of a descending chain of centralizers. In this paper we complete a description of centralizers for unimodular $GBS$ groups. This allows us to find the centralizer dimension of all $GBS$ groups and to establish a way to compute it.
Keywords: centralizer of set of elements, centralizer dimension, generalized Baumslag–Solitar group, Baumslag–Solitar group. 
F. A. Dudkin. Computation of the centralizer dimension of generalized Baumslag–Solitar groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1823-1841. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a33/
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     title = {Computation of the centralizer dimension of generalized {Baumslag{\textendash}Solitar} groups},
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