UBIQUITY OF FREE SUBGROUPS

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,...

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Veröffentlicht in:	The Bulletin of the London Mathematical Society 2003-09, Vol.35 (5), p.624-634
Hauptverfasser:	GARTSIDE, P. M., KNIGHT, R. W.
Format:	Artikel
Sprache:	eng
Schlagworte:	Notes and Papers
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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).
ISSN:	0024-6093 1469-2120
DOI:	10.1112/S0024609303002194