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https://hdl.handle.net/10316/43884
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: | 2013 | Publisher: | Springer | Project: | PEst-C/MAT/UI0324/2011 | Serial title, monograph or event: | Israel Journal of Mathematics | Volume: | 196 | Issue: | 1 | 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 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. | URI: | https://hdl.handle.net/10316/43884 | DOI: | 10.1007/s11856-012-0139-4 10.1007/s11856-012-0139-4 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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Almeida-Costa_Presentations_of_Schutzenberger_groups_of_subshifts-v3.pdf | 306.5 kB | Adobe PDF | View/Open |
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