Presentations of Schutzenberger groups of minimal subshifts

• Tipo: Artigo em Revista Científica Internacional
• Data: 2013

Autores

Jorge Almeida (Autor) FCUP; Alfredo Costa (Autor) Outra

Revista

Título: Israel Journal of Mathematics

Vol. 196

Páginas: 1-31

ISSN: 0021-2172

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 11 Citações

Scopus - 12 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica