Self-similarity of the generalized Baumslag-Solitar groups

Abstract

We show that all residually finite generalized Baumslag-Solitar groups of rank $n \geq 1$, defined on a finite and connected graph, are self-similar. Furthermore we prove that all residually finite fundamental groups of (finite, connected) graph of groups where all vertex and edge groups are torsion-free and commensurable with the Heisenberg group and all edge groups properly embed in the corresponding vertex groups are self-similar.