QUOTIENT AUTOMATION ACCORDING TO A DIRECT FACTOR OF AN AUTOMORPHISM GROUP

To each subgroup H of the automorphism group of an automaton we may assign the quotient automaton modulo H, if we define the sets of transitivity under H as its internal states. For strongly connected automata, whose automorphism group has a direct product H×L as subgroup, we prove that the quotient group of this automorphism subgroup modulo H is isomorphic to a automorphism group of the quotient automaton modulo H. © 1966 Springer-Verlag.