Torsion in the outer automorphism groups of generalized Baumslag–Solitar groups

A generalized Baumslag–Solitar group ($GBS$-group) is a finitely generated group acting on a tree with infinite cyclic edge and vertex stabilizers. It is known that the outer automorphism groups of some $GBS$ groups contain some $p$-torsion of unbounded order. We prove that in this case the prime $p$ divides the integral modulus of $G$. This result answers Levitt's question.