Self‐similarity of the generalized Baumslag–Solitar groups

Key Points

• This research investigates the self-similarity of residually finite generalized Baumslag–Solitar groups defined on finite graphs.
• Examined generalized Baumslag–Solitar groups based on finite and connected graphs.
• Analyzed conditions under which vertex and edge groups maintain specific properties.
• Considered vertex and edge groups being torsion-free and commensurable with the Heisenberg group.
• Demonstrated that all examined residually finite Baumslag–Solitar groups are self-similar.
• Established that certain graph of groups also exhibit self-similarity under specific conditions.