Group laws and free subgroups in topological groups

Details Group laws and free subgroups in topological groups Group laws and free subgroups in topological groups

2003-06-25

arxiv.org/abs/math/0306364v1

Mathematics

Group Theory

10 pages

Scientific paper

We prove 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 we show that almost all finite subsets of the group generate free subgroups. We derive consequences of these theorems on Thompson's group $F$, weakly branch groups, automorphism groups of regular trees and profinite groups with alternating composition factors of unbounded degree.

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