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arXiv · 1805.02596

Normal amenable subgroups of the automorphism group of sofic shifts

Kitty Yang
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Abstract

Let $(X, \sigma)$ be a transitive sofic shift and let $\rm{Aut}(X)$ denote its automorphism group. We generalize a result of Frisch, Schlank, and Tamuz to show that any normal amenable subgroup of $\rm{Aut}(X)$ 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.

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Kitty Yang. 2018-05-07. Normal amenable subgroups of the automorphism group of sofic shifts. https://doi.org/10.1017/etds.2020.4

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