Algebra, Logic and Topology

 

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Author(s)
Alfredo Costa; Benjamin Steinberg;

Title
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.

Preprint series
Pré-publicações do Departamento de Matemática da Universidade de Coimbra

Issue
09-28

Year
2009

 
     
 

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