High transitivity for more groups acting on trees

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

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]
4 LMBP - Laboratoire de Mathématiques Blaise Pascal

We establish a new sharp sufficient condition for groups acting on trees to be highly transitive. 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. High transitivity for more groups acting on trees. 2020. ⟨hal-02518983v1⟩