Free subgroups in groups acting on rooted trees Academic Article uri icon


  • 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 existsw 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. European Mathematical Society.

published proceedings


author list (cited authors)

  • Nekrashevych, V.

citation count

  • 15

complete list of authors

  • Nekrashevych, Volodymyr

publication date

  • January 2010