Group Laws and Free Subgroups in Topological Groups

By Miklós Abért. 2003

61 citations recorded by the source corpus.

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. 2000 Mathematics Subject Classification 20B07, 20E10, 20E18, 20P05.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2bb0223de0000fa6e72123eaf0702e904606fa83

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Amenable actions, free products and a fixed point property (2005, background): “The idea that generic transformations generate a free group has been used in, for example, [10, 8, 13, 2, 1].”
Combinatorial algebra : syntax and semantics (2014, unknown): “I would like to thank Miklos Abért,, Laurent Bartholdi , Alexei Belov-Kanel, George Bergman, Mikhail Ershov, Rostislav Grigorchuk, Yves Guivarc’h, 9 Susan Hermiller, Tony Huynh, David Galvin, Alexei Krasilnikov, Gerry Myerson, Ralph McKenzie, George McNulty, Sasho Nikolov, Jan Okniński, Alexander ”
Branch rings, thinned rings, tree enveloping rings (2004, background): “for every w 6= 1 in the free group F(y1, . . . , yk) there exist g1, . . . , gk ∈ G with w(g1, . . . , gk) 6= 1. We quote the following general result, due to Mikl´os Ab´ert: Proposition 2.4 ([ 2, Theorem 1 ]).”
Some topics in the dynamics of group actions on rooted trees (2011, background): “These issues are discussed, in particular, in [3, 79, 80, 82, 153, 6, 1, 13] and other publications.”