{"paper":{"title":"$p$-groups with exactly four codegrees","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":"2019-01-22T15:42:21Z","abstract_excerpt":"Let $G$ be a $p$-group and let $\\chi$ be an irreducible character of $G$. The codegree of $\\chi$ is given by $|G:\\text{ker}(\\chi)|/\\chi(1)$. Du and Lewis have shown that a $p$-group with exactly three codegrees has nilpotence class at most 2. Here we investigate $p$-groups with exactly four codegrees. If, in addition to having exactly four codegrees, $G$ has two irreducible character degrees, $G$ has largest irreducible character degree $p^2$, $|G:G'|=p^2$, or $G$ has coclass at most 3, then $G$ has nilpotence class at most 4. In the case of coclass at most 3, the order of $G$ is bounded by $p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07425","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"}