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Closed subgroups of free profinite monoids are projective profinite groups

Closed subgroups of free profinite monoids are projective profinite groups 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Oxford University Press

Closed subgroups of free profinite monoids are projective profinite groups

Closed subgroups of free profinite monoids are projective profinite groups

Bulletin of the London Mathematical Society , Volume 40 (3) – Jun 1, 2008

Abstract

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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References (28)

Publisher
Oxford University Press
Copyright
© 2008 London Mathematical Society
Subject
PAPERS
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bdn017
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Bulletin of the London Mathematical SocietyOxford University Press

Published: Jun 1, 2008

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