Invariant random subgroups of lamplighter groups

Lewis Bowen*, Rostislav Grigorchuk, Rostyslav Kravchenko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

Let G be one of the lamplighter groups (Formula presented.) and Sub(G) the space of all subgroups of G. We determine the perfect kernel and Cantor-Bendixson rank of Sub(G). The space of all conjugation-invariant Borel probability measures on Sub(G) is a simplex. We show that this simplex has a canonical Poulsen subsimplex whose complement has only a countable number of extreme points. If F is a finite group and Γ an infinite group which does not have property (T), then the conjugation-invariant probability measures on Sub(Formula presented.) supported on (Formula presented.) also form a Poulsen simplex.

Original languageEnglish (US)
Pages (from-to)763-782
Number of pages20
JournalIsrael Journal of Mathematics
Volume207
Issue number2
DOIs
StatePublished - Apr 27 2015

ASJC Scopus subject areas

  • Mathematics(all)

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