Geodesic
Free subgroups in groups acting on rooted trees
Volodymyr V. Nekrashevych1 orcid
1Texas A&M University, College Station, United States
Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 847-862

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DOI

We show that if a group G acting faithfully on a rooted tree T has a free subgroup, then either there exists a point w of the boundary ∂T and a free subgroup of G with trivial stabilizer of w, or there exists w∈∂T and a free subgroup of G fixing w and acting faithfully on arbitrarily small neighborhoods of w. This can be used to prove the absence of free subgroups for different known classes of groups. For instance, we prove that iterated monodromy groups of expanding coverings have no free subgroups and give another proof of a theorem by S. Sidki.
DOI : 10.4171/ggd/110
Classification : 20-XX, 00-XX
Mots-clés : Groups acting on rooted trees, free subgroups, boundary of a tree, group of germs

Volodymyr V. Nekrashevych  1

1 Texas A&M University, College Station, United States 
Volodymyr V. Nekrashevych. Free subgroups in groups acting on rooted trees. Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 847-862. doi: 10.4171/ggd/110
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/110/}
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