On the group of a rational maximal bifix code

Jorge Almeida 1 , Alfredo Costa 2 , Revekka Kyriakoglou 3  and Dominique Perrin 3
  • 1 Departamento de Matemática, Universidade do Porto, CMUP, Porto, Portugal
  • 2 Department of Mathematics, University of Coimbra, CMUC, Coimbra, Portugal
  • 3 Université Paris-Est, LIGM, Marne La Vallée, France
Jorge Almeida
  • CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal
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, Alfredo Costa
  • Corresponding author
  • CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001-501, Coimbra, Portugal
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, Revekka Kyriakoglou and Dominique Perrin

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 ZF, when F is recurrent and ZF is rational. The case where F is uniformly recurrent, which is known to imply the finiteness of ZF, 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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