On the Centralizer Dimension and Lattice of Generalized Baumslag–Solitar Groups

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Abstract

A generalized Baumslag–Solitar group (a GBS group) is a finitely generated group G acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups. Each GBS group is the fundamental group π1(A) of some labeled graph A. We describe the centralizers of elements and the centralizer lattice. Also, we find the centralizer dimension for GBS groups if A is a labeled tree.

Original languageEnglish
Pages (from-to)403-414
Number of pages12
JournalSiberian Mathematical Journal
Volume59
Issue number3
DOIs
Publication statusPublished - 1 May 2018

Keywords

  • centralizer dimension
  • centralizer lattice
  • generalized Baumslag–Solitar group
  • generalized Baumslag-Solitar group

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