On the group of a rational maximal bifix code

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 $Z\cap F$, when $F$ is recurrent and $Z\cap F$ is rational. The case where $F$ is uniformly recurrent, which is known to imply the finiteness of $Z\cap F$, receives special attention. The proofs are done by exploring the connections with the structure of the free profinite monoid over the alphabet of $F$.

References in corpus (4)

• Acyclic, connected and tree sets
• A geometric interpretation of the Schützenberger group of a minimal subshift
• The linear nature of pseudowords
• Equidivisible pseudovarieties of semigroups

Cited by in corpus (2)

• A profinite approach to complete bifix decodings of recurrent languages
• Symbolic dynamics and semigroup theory