On the automorphism group of a reduced automaton

In this paper we shall investigate the automorphism group G(A/H) of the reduced automaton A/H where A = (S, I, M) is a finite strongly connected automaton and H is a subgroup of the automorphism group G(A) of the automaton A. This problem and other related topics have been dealt with recently by G. P. Weeg, A. C. Fleck, and B. Barnes.1,2,3,4,5 However, the particular problem to give an isomorphic representation of G(A/H) for arbitrary A and H still remained open. Our present purpose is to fill this gap.