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\cap F} , when F is recurrent and Z ∩ F {Z\cap F} is rational. The case where F is uniformly recurrent, which is known to imply the finiteness of Z ∩ F {Z\cap 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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