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Bulletin of the London Mathematical Society 2005 37(1):75-79; doi:10.1112/S0024609304003972
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© London Mathematical Society

Almost All Finitely Generated Subgroups of the Nottingham Group are Free

Balázs Szegedy

Alfréd Rényi Institute of Mathematics 1364 Budapest, P.O. Box 127, Hungary; szegedy{at}renyi.hu

Received 7 June 2002. Revision received 13 August 2003.

It is proved that two random elements of the Nottingham group generate a free group with probability 1. This answers a question of A. Shalev. 2000 Mathematics Subject Classification 20E18, 13F25.

This research was partially supported by the Hungarian National Research Foundation (OTKA), grant no. T038059, and by Microsoft Research.


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