Profinite Groups Associated to Sofic Shifts are Free

Abstract

We show that the maximal subgroup of the free profinite semigroup associated by Almeida to an irreducible sofic shift is a free profinite group, generalizing an earlier result of the second author for the case of the full shift (whose corresponding maximal subgroup is the maximal subgroup of the minimal ideal). A corresponding result is proved for certain relatively free profinite semigroups. We also establish some other analogies between the kernel of the free profinite semigroup and the $\J$-class associated to an irreducible sofic shift.

References in corpus (2)

• Closed subgroups of free profinite monoids are projective profinite groups
• A Combinatorial Property of Ideals in Free Profinite Monoids

Cited by in corpus (7)

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• Freeness of Schützenberger groups of primitive substitutions
• A profinite approach to complete bifix decodings of recurrent languages