{"paper":{"title":"$p$-groups with $p^2$ as a codegree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark L. Lewis, Sarah Croome","submitted_at":"2018-11-07T18:18:30Z","abstract_excerpt":"Let $G$ be a $p$-group and let $\\chi$ be an irreducible character of $G$. The codegree of $\\chi$ is given by $|G:\\text{ker}(\\chi)|/\\chi(1)$. This paper investigates the relationship between the nilpotence class of a group and the inclusion of $p^2$ as a codegree. If $G$ is a finite $p$-group with coclass $2$ and order at least $p^5$, or coclass $3$ and order at least $p^6$, then $G$ has $p^2$ as a codegree. With an additional hypothesis this result can be extended to $p$-groups with coclass $n\\ge 3$ and order at least $p^{2n}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03057","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"}