Computation of the centralizer dimension of generalized Baumslag-Solitar groups

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2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1823-1841
Number of pages19
JournalСибирские электронные математические известия
Publication statusPublished - 1 Jan 2018


  • Baumslag-Solitar group
  • Centralizer dimension
  • Centralizer of set of elements
  • Generalized Baumslag-Solitar group


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