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

 

A property of subgroups of infinite index in a free group


Author: G. N. Arzhantseva
Journal: Proc. Amer. Math. Soc. 128 (2000), 3205-3210
MSC (2000): Primary 20E07, 20F06, 20P05.
Published electronically: May 11, 2000
MathSciNet review: 1694447
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Abstract:

We prove that if $H$ is a finitely generated subgroup of infinite index in a free group $F_m$, then, in a certain statistical meaning, the normal subgroup generated by ``randomly'' chosen elements $r_1,\dots ,r_n$of $F_m$ has trivial intersection with $H$.


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Additional Information

G. N. Arzhantseva
Affiliation: Section de Mathématiques, Université de Genève, CP 240, 1211 Genève 24, Switzerland
Email: Goulnara.Arjantseva@math.unige.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05508-8
PII: S 0002-9939(00)05508-8
Keywords: Free groups, generic properties of groups, labelled graphs
Received by editor(s): January 15, 1999
Published electronically: May 11, 2000
Additional Notes: The work is supported by the Russian Foundation for Fundamental Research grant 96-01-0420 and by ISSEP grant a98-2146.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 2000 American Mathematical Society