Normal amenable subgroups of the automorphism group of sofic shifts

Abstract

Let $(X,\sigma )$ be a transitive sofic shift and let $\mathrm{Aut}(\mathrm{X})$ denote its automorphism group. We generalize a result of Frisch, Schlank, and Tamuz to show that any normal amenable subgroup of $\mathrm{Aut}(\mathrm{X})$ must be contained in the subgroup generated by the shift. We also show that the result does not extend to higher dimensions by giving an example of a two-dimensional mixing shift of finite type whose automorphism group is amenable and not generated by the shift maps.

Change in title due to major theorem upgrade; extends result from SFTs to sofic shifts

References in corpus (1)

• Normal amenable subgroups of the automorphism group of the full shift