  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.
