Ramification structures for quotients of the Grigorchuk groups

TL;DR

This paper demonstrates that infinitely many quotients of the Grigorchuk groups possess ramification structures, providing the first explicit family of 3-generated finite 2-groups with this property.

Contribution

It establishes the existence of an infinite family of 3-generated finite 2-groups with ramification structures, expanding understanding of group-theoretic properties related to surface isogenous groups.

Findings

Infinitely many quotients of Grigorchuk groups admit ramification structures.

First explicit family of 3-generated finite 2-groups with ramification structures.

Connects group quotients to geometric surface properties.

Abstract

Groups associated to surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a 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.