An algorithm to compute the Hausdorff dimension of regular branch groups

TL;DR

This paper presents an explicit algorithm for calculating the Hausdorff dimension of regular branch groups, implemented in GAP, and applied to GGS-groups acting on the 4-adic tree.

Contribution

The paper introduces a novel algorithm for Hausdorff dimension computation of regular branch groups and provides its implementation and application to specific GGS-groups.

Findings

Algorithm successfully computes Hausdorff dimensions

Implementation in GAP demonstrates practical applicability

Applied to GGS-groups on 4-adic tree with concrete results

Abstract

An explicit algorithm is given for the computation of the Hausdorff dimension of the closure of a regular branch group in terms of an arbitrary branch structure. We implement this algorithm in GAP and apply it to a family of GGS-groups acting on the 4-adic tree.