{"paper":{"title":"On prime divisors of character degrees and codegrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Dongfang Yang","submitted_at":"2026-06-25T14:09:56Z","abstract_excerpt":"Let $G$ be a finite group, and let $\\mathrm{Irr}(G)$ denote the set of irreducible complex characters of $G$. For $\\epsilon\\in \\{ \\pm \\}$, we define $\\mathrm{cd}_{\\epsilon}(G)=\\{ \\chi_{\\epsilon}(1)\\mid \\chi\\in \\mathrm{Irr}(G) \\}$, where $\\chi_{+}(1)=\\chi(1)$ denotes the degree of $\\chi$, $\\chi_{-}(1)=|G:\\ker(\\chi)|/\\chi(1)$ denotes the codegree of $\\chi$. Further, let $\\omega_{\\epsilon}(G)=\\{ \\pi(n)\\mid n\\in \\mathrm{cd}_{\\epsilon}(G) \\}$, where $\\pi(n)$ stands for the set of prime divisors of $n$. We established that if $|\\omega_{\\epsilon}(G)|\\leq 3$, then $G$ is solvable. Additionally, a gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27065","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27065/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"}