Presentations of Schützenberger groups of minimal subshifts

• Autor(a) principal: Almeida, Jorge
• Data de Publicação: 2013
• Outros Autores: Costa, Alfredo
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/43884; https://doi.org/10.1007/s11856-012-0139-4
• topic: Profinite group presentation; Free profinite semigroup; Subshift; Prouhet-Thue-Morse substitution

In previous work, the first author established a natural bijection between minimal subshifts and maximal regular J -classes of free profinite semigroups. In this paper, the Schützenberger groups of such J -classes are investigated, in particular in respect to a conjecture proposed by the first author concerning their profinite presentation. The conjecture is established for all non-periodic minimal subshifts associated with substitutions. It entails that it is decidable whether a finite group is a quotient of such a profinite group. As a further application, the Schützenberger group of the J -class corresponding to the Prouhet-Thue-Morse subshift is shown to admit a somewhat simpler presentation, from which it follows that it has rank three, and that it is non-free relatively to any pseudovariety of groups.