On the group of a rational maximal bifix code.

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 n F,when F is recurrent and Z n F is rational. The casewhere F is uniformly recurrent, which is known to imply the finiteness of Z n 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. [ABSTRACT FROM AUTHOR]