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Corpus ID: 189762272

Triple transitivity and non-free actions in dimension one

@article{Boudec2019TripleTA,
title={Triple transitivity and non-free actions in dimension one},
author={A. L. Boudec and Nicol'as Matte Bon},
journal={arXiv: Group Theory},
year={2019}
}

We show that if $G$ is either: (1) a group of homeomorphisms of the circle such that the action of $G$ on $S^1$ is minimal, proximal, non-topologically free and satisfies some mild assumption; (2) a group of automorphisms of a tree $T$ such that the action of $G$ on the boundary $\partial T$ is minimal and non-topologically free; then the following holds: every 3-transitive faithful action of $G$ on a set is conjugate to the action on an orbit in $S^1$ or $\partial T$. As a corollary, we obtain… CONTINUE READING