The derived series of GGS-groups

Abstract

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

arXiv comment20 pages. Version 2 contains a correction to the statement of Theorem 1.2