Premium
Closed subgroups of free profinite monoids are projective profinite groups
Author(s) -
Rhodes John,
Steinberg Benjamin
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn017
Subject(s) - profinite group , mathematics , monoid , pure mathematics , class (philosophy) , group (periodic table) , computer science , physics , artificial intelligence , quantum mechanics
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.