Non-abelian free groups admit non-essentially free actions on rooted trees

Miklos Abert; Gabor Elek

Non-abelian free groups admit non-essentially free actions on rooted trees

Group Theory 2007-07-19 v2 Combinatorics

Authors: Miklos Abert , Gabor Elek

Abstract

We show that every countable non-abelian free group $\Gamma$ admits a spherically transitive action on a rooted tree $T$ such that the action of $\Gamma$ on the boundary of $T$ is not essentially free. This reproves a result of Bergeron and Gaboriau. The existence of such an action answers a question of Grigorchuk, Nekrashevich and Sushchanskii.

Keywords

group actions group theory

Cite

@article{arxiv.0707.0970,
  title  = {Non-abelian free groups admit non-essentially free actions on rooted trees},
  author = {Miklos Abert and Gabor Elek},
  journal= {arXiv preprint arXiv:0707.0970},
  year   = {2007}
}