On the isomorphism problem for generalized Baumslag-Solitar groups: invariants and flexible configurations

TL;DR

This paper addresses the isomorphism problem for a specific class of generalized Baumslag-Solitar groups, introducing invariants that enable a decision procedure for their isomorphism.

Contribution

It introduces a new family of invariants that fully characterize isomorphism classes of GBS groups with certain properties, making the problem decidable.

Findings

Isomorphism problem is decidable for GBS groups with one quasi-conjugacy class.

Introduces invariants that fully characterize isomorphism within this class.

Provides a decision procedure based on these invariants.

Abstract

We prove that the isomorphism problem is decidable for generalized Baumslag-Solitar (GBS) groups with one quasi-conjugacy class and full support gaps. In order to do so we introduce a family of invariants that fully characterize the isomorphism within this class of GBSs.