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Ubiquity of Free Subgroups
Author(s) -
Gartside P. M.,
Knight R. W.
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002194
Subject(s) - mathematics , free product , unitary state , profinite group , free group , rank (graph theory) , topological group , group (periodic table) , normal subgroup , combinatorics , permutation group , pure mathematics , permutation (music) , topology (electrical circuits) , chemistry , physics , organic chemistry , political science , acoustics , law
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).