Authors: Lewis Bowen Rostislav Grigorchuk Rostyslav Kravchenko
Publish Date: 2015/02/17
Volume: 207, Issue: 2, Pages: 763-782
Abstract
Let G be one of the lamplighter groups Bbb Z/pBbb Zn wr Bbb Z and SubG the space of all subgroups of G We determine the perfect kernel and CantorBendixson rank of SubG The space of all conjugationinvariant Borel probability measures on SubG 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 conjugationinvariant probability measures on SubF wr Gamma supported on oplus Gamma F also form a Poulsen simplex
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