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Article Dans Une Revue Journal of the London Mathematical Society Année : 2022

Triple transitivity and non-free actions in dimension one

Résumé

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 sharp upper bounds for the transitivity degree of these groups. These results produce new classes of infinite groups whose transitivity degree is known. In the Appendix we show that if a group satisfies a non-trivial mixed identity, then either it contains a normal subgroup isomorphic to a finitary alternating group, or it has finite transitivity degree.

Dates et versions

hal-02381983 , version 1 (26-11-2019)

Identifiants

Citer

Adrien Le Boudec, Nicolás Matte Bon. Triple transitivity and non-free actions in dimension one. Journal of the London Mathematical Society, 2022, 105 (2), pp.884-908. ⟨10.1112/jlms.12521⟩. ⟨hal-02381983⟩
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