Ramification structures for quotients of the Grigorchuk groups

Groups associated to surfaces isogenous to a higher product of curves can be characterized by a purely group-theoretic condition, which is the existence of the so-called ramification structure. In this paper, we prove that infinitely many quotients of the Grigorchuk groups admit ramification structures. This gives the first explicit infinite family of 3-generated finite 2-groups with ramification structures.