The isomorphism problem for small-rose generalized Baumslag-Solitar groups

TL;DR

This paper proves that the isomorphism problem can be solved for a specific class of generalized Baumslag-Solitar groups called small rose non-ascending groups, advancing understanding of their algebraic structure.

Contribution

It demonstrates the solvability of the isomorphism problem for small rose non-ascending generalized Baumslag-Solitar groups, a previously unresolved case.

Findings

Isomorphism problem is solvable for small rose non-ascending generalized Baumslag-Solitar groups.

Provides an algorithmic solution for this class of groups.

Enhances understanding of the structure and classification of these groups.

Abstract

A generalized Baumslag-Solitar group is a finitely generated group that acts on a tree with infinite-cyclic vertex and edge stabilizers. In this paper, we show that the isomorphism problem is solvable for small rose non-ascending generalized Baumslag- Solitar groups.