The intersections of the lower central series and the subgroups of finite p-index of Generalized Baumslag-Solitar tree groups

For a Generalized Baumslag-Solitar group $G$ with underling graph a tree, we calculate the intersection ${\gamma }_{\omega }(G)$ of the lower central series and the intersection $(N_p{)}_{\omega }(G)$ of the subgroups of finite index some power of a prime $p$.