Mappings of group shifts

A group shift is a proper closed shift-invariant subgroup of G(Z2) where G is a finite group. We consider a class of group shifts in which G is a fini te field and show that mixing is a necessary and sufficient condition on su ch a group shift for all codes from it into another group shift to be affin e and all codes from another group shift into it to be affine. As a corolla ry, it will follow for G = Z(p) that two mixing group shifts are topologica lly conjugate if and only if they are equal.