Closed subgroups of free profinite monoids are projective profinite groups

Details Closed subgroups of free profinite monoids are projective profinite groups Closed subgroups of free profinite monoids are projective profinite groups

2006-11-29

arxiv.org/abs/math/0611896v1

Mathematics

Group Theory

Scientific paper

We prove that the class of closed subgroups of free profinite monoids is precisely the class of projective profinite groups. In particular, the profinite groups associated to minimal symbolic dynamical systems by Almeida are projective. Our result answers a question raised by Lubotzky during the lecture of Almeida at the Fields Workshop on Profinite Groups and Applications, Carleton University, August 2005. We also prove that any finite subsemigroup of a free profinite monoid consists of idempotents.

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