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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On quasifree profinite groups


Authors: Luis Ribes, Katherine Stevenson and Pavel Zalesskii
Journal: Proc. Amer. Math. Soc. 135 (2007), 2669-2676
MSC (2000): Primary 20E18; Secondary 14G32
Published electronically: February 9, 2007
MathSciNet review: 2317938
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Abstract: Recently, it has been shown by Harbater and Stevenson that a profinite group $ G$ is free profinite of infinite rank $ m$ if and only if $ G$ is projective and $ m$-quasifree. The latter condition requires the existence of $ m$ distinct solutions to certain embedding problems for $ G$. In this paper we provide several new non-trivial examples of $ m$-quasifree groups, projective and non-projective. Our main result is that open subgroups of $ m$-quasifree groups are $ m$-quasifree.


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Additional Information

Luis Ribes
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: lribes@math.carleton.ca

Katherine Stevenson
Affiliation: Department of Mathematics, California State University Northridge, Northridge, California 91330
Email: katherine.stevenson@csun.edu

Pavel Zalesskii
Affiliation: Department of Mathematics, University of Brasília, Brasília, Brazil
Email: pz@mat.unb.br

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08892-2
PII: S 0002-9939(07)08892-2
Received by editor(s): May 3, 2006
Published electronically: February 9, 2007
Additional Notes: The first author was partially supported by an NSERC grant
The second author was partially supported by an NSF grant
The third author was partially supported by CAPES and CNPq
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2007 American Mathematical Society