Profinite groups associated to sofic shifts are free

• Author(s): Costa, Alfredo ; Steinberg, Benjamin
• Date: 2009
• Persistent ID: http://hdl.handle.net/10316/11160
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Free profinite semigroups; Free profinite groups; Sofic shifts; Symbolic dynamics
• Document Type: Preprint
• Language: English

Description

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. Research programme AutoMathA of ESF; FCT project PTDC/MAT/65481/2006 and FCT post-doctoral grant SFRH/BPD/46415/2008; NSERC; DFG