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UBIQUITY OF FREE SUBGROUPS

Published online by Cambridge University Press:  13 August 2003

P. M. GARTSIDE  and
R. W. KNIGHT
P. M. GARTSIDE
Affiliation:
Department of Mathematics, University of Pittsburgh, USAgartside@math.pitt.edu
R. W. KNIGHT
Affiliation:
Mathematical Institute, Oxford University, 24–29 St Giles, Oxford OXI 3LB, knight@maths.ox.ac.uk
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Abstract

Necessary and sufficient conditions are given for a Polish topological group to be ‘almost free’. It is deduced that the existence of one free subgroup of a Polish group can lead to the existence of many free subgroups of maximal rank. Applications are given to permutation groups, profinite groups, Lie groups and unitary groups.

Keywords

22F5020E0554H05 (primary)12F1020B2720B3020E18 (secondary)
Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 5 , September 2003 , pp. 624 - 634
Copyright
© The London Mathematical Society 2003

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