Presentations of Schutzenberger groups of minimal subshifts

• Type: Article in International Scientific Journal
• Date: 2013

Authors

Jorge Almeida (Author) FCUP; Alfredo Costa (Author) Other

Journal

Title: Israel Journal of Mathematics

Vol. 196

Pages: 1-31

ISSN: 0021-2172

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 11 Citations

Scopus - 12 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-006-8AD

DOI: 10.1007/s11856-012-0139-4

Abstract (EN): 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 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 Schutzenberger 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.

Language: English

Type (Professor's evaluation): Scientific