Profinite groups associated with weakly primitive substitutions

• Type: Article in International Scientific Journal
• Date: 2007

Authors

Almeida, J (Author) FCUP

Journal

Title: Journal of Mathematical Sciences

Vol. 144

Pages: 3881-3903

ISSN: 1072-3374

Publisher: Springer Nature

Indexing

ISI Web of Knowledge

Scopus - 7 Citations

Other information

Authenticus ID: P-007-HVA

DOI: 10.1007/s10958-007-0242-y

Abstract (EN): A uniformly recurrent pseudoword is an element of a free profinite semigroup in which every finite factor appears in every sufficiently long finite factor. An alternative characterization is as a pseudoword that is a factor of all its infinite factors, i.e., one that lies in a script J sign -class with only finite words strictly script J sign -above it. Such a script J sign -class is regular, and therefore it has an associated profinite group, namely, any of its maximal subgroups. One way to produce such script J sign -classes is to iterate finite weakly primitive substitutions. This paper is a contribution to the computation of the profinite group associated with the script J sign-class that is generated by the infinite iteration of a finite weakly primitive substitution. The main result implies that the group is a free profinite group provided the substitution induced on the free group on the letters that appear in the images of all of its sufficiently long iterates is invertible. © Springer Science+Business Media, Inc. 2007.

Language: English

Type (Professor's evaluation): Scientific