$$\mathcal {F}_\pi $$-residuality of generalized Baumslag–Solitar groups

Abstract

A generalized Baumslag–Solitar group is a finitely generated group that acts on a tree with infinite cyclic edge and vertex stabilizers. A group G is residually a finite $$\pi $$-group, for a set of primes $$\pi $$, if every non-trivial element of G has non-trivial image in a quotient of G that is a finite $$\pi $$-group. We provide a criterion for generalized Baumslag–Solitar groups to be residually a finite $$\pi $$-group.