I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2005, VOLUME 11, NUMBER 3, PAGES 13-48
Profinite groups associated with weakly primitive substitutions
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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 -class with only finite words strictly
Such a -class is regular, and therefore it has an
associated profinite group, namely any of its maximal subgroups.
One way to produce such -classes is to iterate finite weakly primitive
This paper is a contribution to the computation of the profinite
group associated with the -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
Last modified: September 14, 2005