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. 
@article{SEMR_2018_15_a33,
     author = {F. A. Dudkin},
     title = {Computation of the centralizer dimension of generalized {Baumslag--Solitar} groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1823--1841},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a33/}
}
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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/