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UBIQUITY OF FREE SUBGROUPS

Published online by Cambridge University Press:  13 August 2003

P. M. GARTSIDE
Affiliation:
Department of Mathematics, University of Pittsburgh, [email protected]
R. W. KNIGHT
Affiliation:
Mathematical Institute, Oxford University, 24–29 St Giles, Oxford OXI 3LB, [email protected]
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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.

Type
Notes and Papers
Copyright
© The London Mathematical Society 2003

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