Presentations of Schutzenberger groups of minimal subshifts

Details Presentations of Schutzenberger groups of minimal subshifts Presentations of Schutzenberger groups of minimal subshifts

2010-01-11

arxiv.org/abs/1001.1475v1

Mathematics

Group Theory

20 pages

Scientific paper

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 Schutzenberger 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.

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