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

Abstract

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 $p$.