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. 2000 Mathematics Subject Classification 22F50, 20E05, 54H05 (primary), 12F10, 20B27, 20B30, 20E18 (secondary).

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