On the groups of codes with empty kernel

Jean Berstel (1) , Clelia de Felice (2) , Dominique Perrin (1) , Giuseppina Rindone (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 DIA - Dipartimento Informatica ed Applicazioni "Renato M. Capocelli"

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.

Domaines: Théorie et langage formel [cs.FL]

Jean Berstel, Clelia de Felice, Dominique Perrin, Giuseppina Rindone. On the groups of codes with empty kernel. Semigroup Forum, 2010, 80 (3), pp.351-374. ⟨hal-00790630⟩