F. A. Dudkin, “On the centralizer dimension and lattice of generalized Baumslag–Solitar groups”, Sibirsk. Mat. Zh., 2018, Volume 59, Number 3,Pages <nobr>514

This article is cited in 7 papers

On the centralizer dimension and lattice of generalized Baumslag–Solitar groups

F. A. Dudkin^ab

^a Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

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 $\pi_1(\mathbb A)$ of some labeled graph $\mathbb A$. We describe the centralizers of elements and the centralizer lattice. Also, we find the centralizer dimension for $GBS$ groups if $\mathbb A$ is a labeled tree.

Keywords: centralizer lattice, centralizer dimension, generalized Baumslag–Solitar group.

UDC: 512.54

MSC: 35R30

Received: 27.04.2017

DOI: 10.17377/smzh.2018.59.303