This article is cited in 5 papers

Mathematical logic, algebra and number theory

Computation of the centralizer dimension of generalized Baumslag–Solitar groups

F. A. Dudkin<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia

Abstract: 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.

UDC: 512.54

MSC: 20E06

Received July 22, 2018, published December 30, 2018

Language: English

DOI: 10.33048/semi.2018.15.147

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