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.
Original language | English |
---|---|
Pages (from-to) | 1823-1841 |
Number of pages | 19 |
Journal | Сибирские электронные математические известия |
Volume | 15 |
DOIs | |
Publication status | Published - 1 Jan 2018 |
Keywords
- Baumslag-Solitar group
- Centralizer dimension
- Centralizer of set of elements
- Generalized Baumslag-Solitar group