# Extensions of Full Shifts with Group Actions

## TL;DR

This paper establishes conditions under which symbolic dynamical systems with countable amenable group actions can be extended from full shifts, generalizing classical results from actions of integers and integer lattices.

## Contribution

It provides a new sufficient condition for symbolic systems with amenable group actions to be extensions of full shifts, broadening the scope of prior work on $bz$ and $bz^d$ actions.

## Key findings

- Identifies a sufficient condition for extension to full shifts
- Generalizes classical results to countable amenable groups
- Advances understanding of symbolic dynamical systems with group actions

## Abstract

We give a sufficient condition for a symbolic topological dynamical system with action of a countable amenable group to be an extension of the full shift, a problem analogous to those studied by Ashley, Marcus, Johnson and others for actions of $\mathbb{Z}$ and $\mathbb{Z}^d$ .