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Title: Presentations of Schützenberger groups of minimal subshifts
Authors: Almeida, Jorge 
Costa, Alfredo 
Keywords: Profinite group presentation; Free profinite semigroup; Subshift; Prouhet-Thue-Morse substitution
Issue Date: 2010
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 10-01 (2010)
Serial title, monograph or event: Pré-Publicações DMUC
Issue: 10-01
Place of publication or event: Coimbra
Abstract: 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.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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