Free subgroups in groups acting on rooted trees
Volodymyr V. Nekrashevych
Texas A&M University, College Station, United States
Abstract
We show that if a group acting faithfully on a rooted tree has a free subgroup, then either there exists a point of the boundary and a free subgroup of with trivial stabilizer of , or there exists and a free subgroup of fixing and acting faithfully on arbitrarily small neighborhoods of . 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.
Cite this article
Volodymyr V. Nekrashevych, Free subgroups in groups acting on rooted trees. Groups Geom. Dyn. 4 (2010), no. 4, pp. 847–862
DOI 10.4171/GGD/110