{"paper":{"title":"Invariant random subgroups of the lamplighter group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Lewis Bowen, Rostislav Grigorchuk, Rostyslav Kravchenko","submitted_at":"2012-06-28T18:00:29Z","abstract_excerpt":"Let $G$ be one of the lamplighter groups $({\\mathbb{Z}/p\\bz})^n\\wr\\mathbb{Z}$ 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 $\\Gamma$ an infinite group which does not have property $(T)$ then the conjugation-invariant probability measures on $\\Sub(F\\wr\\Gamma)$ supported on $\\opl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6780","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}