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On the group of a rational maximal bifix code

Abstract : Abstract We give necessary and sufficient conditions for the group of a rational maximal bifix code Z to be isomorphic with the F -group of Z ∩ F {Z ∪ F} , when F is recurrent and Z ∩ F {Z ∪ F} is rational. The case where F is uniformly recurrent, which is known to imply the finiteness of Z ∩ F {Z ∪ F} , receives special attention. The proofs are done by exploring the connections with the structure of the free profinite monoid over the alphabet of F .
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Submitted on : Saturday, May 15, 2021 - 10:27:14 PM
Last modification on : Friday, June 18, 2021 - 4:02:02 PM

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Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin. On the group of a rational maximal bifix code. Forum Mathematicum, De Gruyter, 2020, 32 (3), pp.553-576. ⟨10.1515/forum-2018-0270⟩. ⟨hal-03226871⟩

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