Multiple conjugacy problem in graphs of free abelian groups

Abstract

A group $G$ is a vGBS group if it admits a decomposition as a nite graph of groups with all edge and vertex groups nitely generated and free abelian. We prove that the multiple conjugacy problem is solvable between two $n$-tuples $A$ and $B$ of elements of $G$ whenever the elements of A does not generate an elliptic subgroup.