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

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

Location: http://mech.math.msu.su/~fpm/eng/k05/k053/k05302h.htm

Last modified: September 14, 2005