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 $\mathscr{B}$-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 $\mathscr{B}$-free subshift is huge whenever $\mathscr{B}\subset \mathbb N$ is infinite and contains no infinite pairwise coprime subset.
From: Aurelia Dymek [view email]
[v1]
Thu, 25 Jun 2026 15:38:01 UTC (28 KB)
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