Factoring strongly irreducible group shift actions onto full shifts of lower entropy

Abstract

We show that if $G$ is a countable amenable group $G$ with the comparison property and $X$ is a strongly irreducible $G$-shift satisfying certain aperiodicity conditions, then $X$ factors onto the full $G$-shift on $N$ symbols, so long as the logarithm of $N$ is less than the topological entropy of $G$.