Highly transitive actions of free products

Soyoung Moon (1, 2) , Yves Stalder (3, 4)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 UB - Université de Bourgogne
3 LMBP - Laboratoire de Mathématiques Blaise Pascal
4 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]

We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group PS_2(Z) (isomorphic to the free product (Z/2Z) *(Z/3Z)) admits a faithful and highly transitive action on a countable set.

Mots clés: Highly transitive actions; Baire category Theorem; Free products

Domaines: Théorie des groupes [math.GR]

Soyoung Moon, Yves Stalder. Highly transitive actions of free products. Algebraic and Geometric Topology, 2013, 13 (1), pp.589-607. ⟨10.2140/agt.2013.13.589⟩. ⟨hal-01902213⟩