On automorphisms of $\mathcal{B}$-admissible and related subshifts

Abstract

We adapt ideas of Kim and Roush [15], originally developed in the study of automorphisms of sofic subshifts, to obtain sufficient conditions under which a subshift has a huge automorphism group. We apply this approach to non-sofic subshifts defined by sets of multiples. In particular, we establish a dichotomy for the $\mathcal{B}$-admissible subshift: its automorphism group is either trivial or contains an embedded copy of the automorphism group of the full shift $\{0,1{\}}^{\mathbb{Z}}$. In the latter case, we say that the automorphism group is huge. We further show that the automorphism group of the hereditary closure of the $\mathcal{B}$-free subshift is huge whenever $\mathcal{B}\subset \mathbb{N}$ is infinite and contains no infinite pairwise coprime subset.

23 pages