Profinite Groups Associated to Sofic Shifts are Free

Details Profinite Groups Associated to Sofic Shifts are Free Profinite Groups Associated to Sofic Shifts are Free

2009-08-04

arxiv.org/abs/0908.0439v1

Mathematics

Group Theory

Scientific paper

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.

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