Amenable Invariant Random Subgroups

Uri Bader (1) , Bruno Duchesne (2) , Jean Lecureux (3)

1 TECHNION - Department of Mathematics
2 IECL - Institut Élie Cartan de Lorraine
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We show that an amenable Invariant Random Subgroup of a locally compact second countable group lives in the amenable radical. This answers a question raised in the introduction of the paper "Kesten's Theorem for Invariant Random Subgroup" by Abert, Glasner and Virag. We also consider, in the opposite direction, property (T), and prove a similar statement for this property. The Appendix by Phillip Wesolek proves that the set of amenable subgroups is a Borel subset in the Chabauty topology.

Mots clés: Invariant Random Subgroup; Amenability; Property (T); relative property (T)

Domaines: Théorie des groupes [math.GR]; Mathématiques générales [math.GM]

Uri Bader, Bruno Duchesne, Jean Lecureux. Amenable Invariant Random Subgroups. 2014. ⟨hal-01064474v2⟩