Profinite Groups Associated to Sofic Shifts are Free
Group Theory
2014-02-26 v1
Abstract
We show that the maximal subgroup of the free profinite semigroup associated by Almeida to an irreducible sofic shift is a free profinite group, generalizing an earlier result of the second author for the case of the full shift (whose corresponding maximal subgroup is the maximal subgroup of the minimal ideal). A corresponding result is proved for certain relatively free profinite semigroups. We also establish some other analogies between the kernel of the free profinite semigroup and the -class associated to an irreducible sofic shift.
Keywords
Cite
@article{arxiv.0908.0439,
title = {Profinite Groups Associated to Sofic Shifts are Free},
author = {Alfredo Costa and Benjamin Steinberg},
journal= {arXiv preprint arXiv:0908.0439},
year = {2014}
}