Presentations of Schützenberger groups of minimal subshifts

• Author(s): Almeida, Jorge ; Costa, Alfredo
• Date: 2010
• Persistent ID: http://hdl.handle.net/10316/13717
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Profinite group presentation; Free profinite semigroup; Subshift; Prouhet-Thue-Morse substitution
• Document Type: Preprint
• Language: English

Description

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 Sch¨utzenberger 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 several types of minimal subshifts associated with substitutions. The Sch¨utzenberger subgroup 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 satisfies the conjecture, that it has rank three, and that it is non-free relatively to any pseudovariety of groups.