Self‐similarity of the generalized Baumslag–Solitar groups

Abstract We show that all residually finite generalized Baumslag–Solitar groups of rank , 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.