A characterization of high transitivity for groups acting on trees

Pierre Fima (1) , François Le Maître (1) , Soyoung Moon (2) , Yves Stalder (3, 4)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 LMBP - Laboratoire de Mathématiques Blaise Pascal
4 UCA - Université Clermont Auvergne

We establish a sharp sufficient condition for groups acting on trees to be highly transitive when the action on the tree is minimal of general type. This give new examples of highly transitive groups, including icc non-solvable Baumslag-Solitar groups, thus answering a question of Hull and Osin.

Domaines: Théorie des groupes [math.GR]

Pierre Fima, François Le Maître, Soyoung Moon, Yves Stalder. A characterization of high transitivity for groups acting on trees. 2021. ⟨hal-02518983v3⟩