A family of fractal non-contracting weakly regular branch groups

TL;DR

This paper introduces a new family of infinite groups acting on d-adic trees that are non-contracting and weakly regular branch over their derived subgroup, expanding the known examples in this area.

Contribution

It constructs the first infinite family of such groups with these properties acting on d-adic trees for any d ≥ 2.

Findings

First example of an infinite family of non-contracting weakly regular branch groups.

Groups act on d-adic trees for any d ≥ 2.

Provides new insights into the structure of branch groups.

Abstract

We construct a new family of groups that is non-contracting and weakly regular branch over the derived subgroup. This gives the first example of an infinite family of groups acting on a $d$-adic tree, with $d \geq 2$, with these properties.