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

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

2007-07-06

arxiv.org/abs/0707.0970v2

Mathematics

Group Theory

Scientific paper

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.

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