{"paper":{"title":"Some reductive anisotropic groups that admit no non-trivial split spherical BN-pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Matthew C. B. Zaremsky, Peter Abramenko","submitted_at":"2011-08-24T19:06:16Z","abstract_excerpt":"We prove, for any infinite field k, that any virtually trivial split spherical BN-pair in the group G(k) of k-rational points of a reductive k-group G is already trivial. We then inspect the case when G is k-anisotropic and show that in many situations G(k) admits no non-trivial split spherical BN-pairs. This improves results and contributes to a conjecture of Caprace and Marquis, which can be viewed as a converse to a well-known result of Borel and Tits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4913","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"}