Normal amenable subgroups of the automorphism group of sofic shifts

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