Profinite Groups Associated with Weakly Primitive Substitutions
نویسنده
چکیده
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 which is a factor of all its infinite factors, that is one which lies in a J -class with only finite words strictly J -above it. Such a J -class is regular and therefore it has an associated profinite group, namely any of its maximal subgroups. One way to produce such J -classes is to iterate finite weakly primitive substitutions. This paper is a contribution to the computation of the profinite group associated with the J -class which 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 which appear in the images of all of its sufficiently long iterates is invertible.
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