Amenable Invariant Random Subgroups

Abstract

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.

We added an Appendix by Phillip Wesolek

References in corpus (4)

• Unimodularity of Invariant Random Subgroups
• Invariant random subgroups of linear groups
• Geometric density for invariant random subgroups of groups acting on CAT(0) spaces
• Shift-minimal groups, fixed price 1, and the unique trace property

Cited by in corpus (11)

• C*-simplicity and the unique trace property for discrete groups
• Stationary C*-dynamical systems
• Unimodularity of Invariant Random Subgroups
• Invariant random subgroups of linear groups
• Subgroup dynamics and $C^{\ast }$-simplicity of groups of homeomorphisms
• Indicability, residual finiteness, and simple subquotients of groups acting on trees
• Geometric density for invariant random subgroups of groups acting on CAT(0) spaces
• Bounding the covolume of lattices in products
• Generic IRS in free groups, after Bowen
• Future directions in locally compact groups
• On the amenable subalgebras of group von Neumann algebras