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GROUP LAWS AND FREE SUBGROUPS IN TOPOLOGICAL GROUPS

Published online by Cambridge University Press:  02 August 2005

MIKLÓS ABÉRT
MIKLÓS ABÉRT
Affiliation:
Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637, USAabert@math.uchicago.edu
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Abstract

A proof is given that a permutation group in which different finite sets have different stabilizers cannot satisfy any group law. For locally compact topological groups with this property, almost all finite subsets of the group are shown to generate free subgroups. Consequences of these theorems are derived for: Thompson's group $F$, weakly branch groups, automorphism groups of regular trees, and profinite groups with alternating composition factors of unbounded degree.

Keywords

20B0720E1020E1820P05
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 4 , August 2005 , pp. 525 - 534
Copyright
© The London Mathematical Society 2005

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Footnotes

Research partially supported by NSF Grant DMS-0401006 and OTKA Grant T38059.