The Isomorphism Problem for Generalized Baumslag–Solitar Groups with One Mobile Edge

Resumo

A generalized Baumslag–Solitar group (GBS group) is a finitely generated group G which acts on a tree with all edge and vertex stabilizers infinite cyclic. Every GBS group is the fundamental group π₁(????) of some labeled graph ????. This paper deals with the isomorphism problem for GBS groups, which is the problem of determining whether π₁(????) ≅ π₁(????) for two given labeled graphs ???? and ????. We describe an algorithm that decides this problem for the case where one of the labeled graphs has a sole mobile edge.