On quasifree profinite groups
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- by Luis Ribes, Katherine Stevenson and Pavel Zalesskii PDF
- Proc. Amer. Math. Soc. 135 (2007), 2669-2676 Request permission
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.References
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- Luis Ribes and Pavel Zalesskii, Profinite groups, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 40, Springer-Verlag, Berlin, 2000. MR 1775104, DOI 10.1007/978-3-662-04097-3
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
- MR Author ID: 245312
- Email: pz@mat.unb.br
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 2669-2676
- MSC (2000): Primary 20E18; Secondary 14G32
- DOI: https://doi.org/10.1090/S0002-9939-07-08892-2
- MathSciNet review: 2317938