Substitutional subshifts and growth of groups

TL;DR

This paper uses symbolic dynamics of Schreier graphs to embed the Grigorchuk group into a simple torsion group with intermediate growth and constructs many different growth types of such groups.

Contribution

It introduces a novel method leveraging symbolic dynamics to embed groups and generate diverse growth types in simple torsion groups.

Findings

Embedded the Grigorchuk group into a simple torsion group of intermediate growth

Constructed uncountably many growth types of simple torsion groups

Demonstrated a new approach using Schreier graphs and symbolic dynamics

Abstract

We show how to use symbolic dynamics of Schreier graphs to embed the Grigorchuk group into a simple torsion group of intermediate growth and to construct uncountably many growth types of simple torsion groups.