2008/02/18 by Volodymyr Nekrashevych, Nekrashevych, Volodymyr · 2 citations
Computer Science · Mathematics · #20E08 #Advanced Graph Theory Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.0802.2554
openalex publication_date 2008/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.