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sofic shift

Ergodic Theory and Dynamical Systems (1)

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1 results

Normal amenable subgroups of the automorphism group of sofic shifts
Part of
- Topological dynamics
KITTY YANG
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 4 / April 2021

Published online by Cambridge University Press:

10 February 2020, pp. 1250-1263

Print publication:

April 2021
- Article
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Let $(X,\unicode[STIX]{x1D70E})$ be a transitive sofic shift and let $\operatorname{Aut}(X)$ denote its automorphism group. We generalize a result of Frisch, Schlank, and Tamuz to show that any normal amenable subgroup of $\operatorname{Aut}(X)$ 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 due to Hochman whose automorphism group is amenable and not generated by the shift maps.