{"paper":{"title":"Centralizers of Subsystems of Fusion Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jason Semeraro","submitted_at":"2014-02-20T12:24:19Z","abstract_excerpt":"When $(S,\\mathcal{F},\\mathcal{L})$ is a $p$-local finite group and $(T,\\mathcal{E},\\mathcal{\\L}_0)$ is weakly normal in $(S,\\mathcal{F},\\mathcal{L})$ we show that a definition of $C_S(\\mathcal{E})$ given by Aschbacher has a simple interpretation from which one can deduce existence and strong closure very easily. We also appeal to a result of Gross to give a new proof that there is a unique fusion system $C_{\\mathcal{F}}(\\mathcal{E})$ on $C_S(\\mathcal{E})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4981","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"}