{"paper":{"title":"The McKay Conjecture on character degrees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Britta Sp\\\"ath, Marc Cabanes","submitted_at":"2024-10-27T09:39:12Z","abstract_excerpt":"We prove that for any prime $\\ell$, any finite group has as many irreducible complex characters of degree prime to $\\ell$ as the normalizers of its Sylow $\\ell$-subgroups. This equality was conjectured by John McKay.\n  The conjecture was reduced by Isaacs--Malle--Navarro (2007) to a conjecture on representations, linear and projective, of finite simple groups that we finish proving here using the classification of those groups.\n  We study mainly characters of normalizers N$_{\\mathbf G}({\\mathbf S})^F$ of Sylow $d$-tori ${\\mathbf S}$ ($d\\geq 3$) in a simply-connected algebraic group ${\\mathbf G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20392","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.20392/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}