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Semigroups and automorphism groups of strongly connected automata

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Abstract

If an automatonA = (X, I, M) is strongly connected,\(\bar I\) is its characteristic semigroup ande is a minimal idempotent of\(\bar I\), then the automorphism groupG(A) ofA is a homomorphic image of a subgroup of the group e\(\bar I\)e (Theorem 3.1) and Theorem 3.3 about the necessary and sufficient conditions ofG(A) to be isomorphic to e\(\bar I\)e Theorems 3.1 and 3.2 make the result by Fleck (1965) more precise. Our method seems completely different from his method. That is, we use the result on regular permutation groups in Burnside's theory of groups of finite order (Theorem 2.1) as new results on the well-known partial ordering of the set of idempotents of a semigroup (Theorems 2.3, 2.5).

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  1. Department of Mathematics, School of Science and Engineering Waseda University, 160, Shinjuku, Tokyo, Japan

    Kenji Uemura

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  1. Kenji Uemura
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Uemura, K. Semigroups and automorphism groups of strongly connected automata. Math. Systems Theory 8, 8–14 (1974). https://doi.org/10.1007/BF01761703

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  • DOI: https://doi.org/10.1007/BF01761703

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