{"paper":{"title":"Normal $p$-complements and irreducible character codegrees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Boru Zhang, Jiakuan Lu, Yu Li","submitted_at":"2021-02-14T11:42:00Z","abstract_excerpt":"Let $G$ be a finite group and $p\\in \\pi(G)$, and let Irr$(G)$ be the set of all irreducible complex characters of $G$. Let $\\chi \\in {\\rm Irr}(G)$, we write ${\\rm cod}(\\chi)=|G:{\\rm ker} \\chi|/\\chi(1)$, and called it the codegree of the irreducible character $\\chi$. Let $N\\unlhd G$, write ${\\rm Irr}(G|N)=\\{\\chi \\in {\\rm Irr}(G)~|~N\\nsubseteq {\\rm ker}\\chi\\}$, and ${\\rm cod}(G|N)=\\{ {\\rm cod}(\\chi) ~|~\\chi\\in{\\rm Irr}(G|N)\\}.$ In this Ipaper, we prove that if $N\\unlhd G$ and every member of ${\\rm cod}(G|N')$ is not divisible by some fixed prime $p\\in \\pi(G)$, then $N$ has a normal $p$-complemen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07132","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/2102.07132/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"}