Freeness of Schützenberger groups of primitive substitutions

Abstract

Our main goal is to study the freeness of Schützenberger groups defined by primitive substitutions. Our findings include a simple freeness test for these groups, which is applied to exhibit a primitive invertible substitution with corresponding non-free Schützenberger group. This constitutes a counterexample to a result of Almeida dating back to 2005. We also give some early results concerning relative freeness of Schützenberger groups, a question which remains largely unexplored.

References in corpus (2)

• Acyclic, connected and tree sets
• A geometric interpretation of the Schützenberger group of a minimal subshift

Cited by in corpus (2)

• Pronilpotent quotients associated with primitive substitutions
• A profinite approach to complete bifix decodings of recurrent languages