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Amenable invariant random subgroups

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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 [2]. We also consider an opposite direction, property (T), and prove a similar statement for this property.

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Authors and Affiliations

  1. Mathematics Department, Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Uri Bader

  2. Institut Élie Cartan de Lorraine, Université de Lorraine B.P. 70239, F-54506, Vandoeuvre-lès-Nancy Cedex, France

    Bruno Duchesne

  3. Département de Mathématiques - Bâtiment 425, Faculté des Sciences d’Orsay Université Paris-Sud 11, F-91405, Orsay, France

    Jean Lécureux

  4. Université catholique de Louvain Institut de Recherche en Mathématiques et Physique (IRMP) Chemin du Cyclotron 2, box L7.01.02, 1348, Louvain-la-Neuve, Belgium

    Phillip Wesolek

Authors
  1. Uri Bader
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  2. Bruno Duchesne
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  3. Jean Lécureux
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  4. Phillip Wesolek
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Correspondence to Bruno Duchesne.

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Bader, U., Duchesne, B., Lécureux, J. et al. Amenable invariant random subgroups. Isr. J. Math. 213, 399–422 (2016). https://doi.org/10.1007/s11856-016-1324-7

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  • DOI: https://doi.org/10.1007/s11856-016-1324-7

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