AUTOMORPHISMS OF Z(D)-SUBSHIFTS OF FINITE-TYPE

Let (SIGMA, sigma) be a Z(d)-subshift of finite type. Under a strong irreducibility condition (strong specification), we show that Aut(SIGMA) contains any finite group. For Z(d)-subshifts of finite type without strong specification, examples show that topological mixing is not sufficient to give any finite group in the automorphism group in general: in particular, End (SIGMA) may be an abelian semigroup. For an example of a topologically mixing Z2-subshift of finite type, the endomorphism semigroup and automorphism group are computed explicitly. This subshift has periodic-point permutations that do not extend to automorphisms.