{"paper":{"title":"Controlling composition factors of a finite group by its character degree ratio","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Hung Ngoc Nguyen, James P. Cossey","submitted_at":"2013-08-05T17:05:11Z","abstract_excerpt":"For a finite nonabelian group $G$ let $\\rat(G)$ be the largest ratio of degrees of two nonlinear irreducible characters of $G$. We show that nonabelian composition factors of $G$ are controlled by $\\rat(G)$ in some sense. Specifically, if $S$ different from the simple linear groups $\\PSL_2(q)$ is a nonabelian composition factor of $G$, then the order of $S$ and the number of composition factors of $G$ isomorphic to $S$ are both bounded in terms of $\\rat(G)$. Furthermore, when the groups $\\PSL_2(q)$ are not composition factors of $G$, we prove that $|G:\\Oinfty(G)|\\leq \\rat(G)^{21}$ where $\\Oinf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1044","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"}