FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 3, PAGES 13-48

Profinite groups associated with weakly primitive substitutions

J. Almeida

Abstract

View as HTML     View as gif image

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 $ \mathcal J $-class with only finite words strictly $ \mathcal J $-above it. Such a $ \mathcal J $-class is regular, and therefore it has an associated profinite group, namely any of its maximal subgroups. One way to produce such $ \mathcal J $-classes is to iterate finite weakly primitive substitutions. This paper is a contribution to the computation of the profinite group associated with the $ \mathcal J $-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.

Main page Contents of the journal News Search

Location: http://mech.math.msu.su/~fpm/eng/k05/k053/k05302h.htm
Last modified: September 14, 2005