The derived series of GGS-groups

Given a GGS-group $G$ with non-constant defining tuple over a prime-regular rooted tree, we calculate the indices $\mathrm{\mid }G:G^{(n)}\mathrm{\mid }$ and describe the structure of the higher derived subgroups $G^{(n)}$ for all $n\in \mathbb{N}$. We find that the values $\mathrm{\mid }G:G^{(n)}\mathrm{\mid }$ depend only mildly on the structure of the defining tuple.