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On the groups of codes with empty kernel

Abstract : An internal factor of a word x is a word v such that x=uvw for some nonempty words u,w. The kernel of a set X of words is the set of words of X which are internal factors of words of X. Let φ be the syntactic morphism of the submonoid X * generated by X. We prove that if X is a code with empty kernel, the groups contained in the image by φ of the complement of the set of internal factors of the words of X are cyclic. This generalizes a result announced by Schützenberger in 1964.
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Submitted on : Wednesday, February 20, 2013 - 4:18:37 PM
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Jean Berstel, Clelia de Felice, Dominique Perrin, Giuseppina Rindone. On the groups of codes with empty kernel. Semigroup Forum, Springer Verlag, 2010, 80 (3), pp.351-374. ⟨hal-00790630⟩



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