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On the groups of codes with empty kernel

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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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Authors and Affiliations

  1. Université Paris Est, LIGM, 77454, Marne-la-Vallée, France

    Jean Berstel, Dominique Perrin & Giuseppina Rindone

  2. Università degli Studi di Salerno, via Ponte Don Melillo, 84084, Fisciano, Italy

    Clelia De Felice

Authors
  1. Jean Berstel
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  2. Clelia De Felice
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  3. Dominique Perrin
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  4. Giuseppina Rindone
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Corresponding author

Correspondence to Jean Berstel.

Additional information

Communicated by Jean-Eric Pin.

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Berstel, J., De Felice, C., Perrin, D. et al. On the groups of codes with empty kernel. Semigroup Forum 80, 351–374 (2010). https://doi.org/10.1007/s00233-010-9214-5

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  • DOI: https://doi.org/10.1007/s00233-010-9214-5

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