Ubiquity of Free Subgroups |
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| Authors: | Gartside P M; Knight R W |
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| Institution: | Department of Mathematics, University of Pittsburgh USA gartside{at}math.pitt.edu
Mathematical Institute, Oxford University 24–29 St Giles, Oxford OXI 3LB, knight{at}maths.ox.ac.uk |
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| Abstract: | Necessary and sufficient conditions are given for a Polish topologicalgroup to be ‘almost free’. It is deduced that theexistence of one free subgroup of a Polish group can lead tothe existence of many free subgroups of maximal rank. Applicationsare given to permutation groups, profinite groups, Lie groupsand unitary groups. 2000 Mathematics Subject Classification22F50, 20E05, 54H05 (primary), 12F10, 20B27, 20B30, 20E18 (secondary). |
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