{"paper":{"title":"On Relative Property (T) and Haagerup's Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Adrian Ioana, Ionut Chifan","submitted_at":"2009-06-29T20:26:56Z","abstract_excerpt":"We consider the following three properties for countable discrete groups $\\Gamma$: (1) $\\Gamma$ has an infinite subgroup with relative property (T), (2) the group von Neumann algebra $L\\Gamma$ has a diffuse von Neumann subalgebra with relative property (T) and (3) $\\Gamma$ does not have Haagerup's property. It is clear that (1) $\\Longrightarrow$ (2) $\\Longrightarrow$ (3). We prove that both of the converses are false."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5363","kind":"arxiv","version":1},"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"}