{"paper":{"title":"Characters of $\\pi'$-degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Carolina Vallejo, Eugenio Giannelli, Mandi Schaeffer Fry","submitted_at":"2019-03-22T17:08:26Z","abstract_excerpt":"Let $G$ be a finite group and let $\\pi$ be a set of primes. Write $\\mathrm{Irr}_{\\pi'}(G)$ for the set of irreducible characters of degree not divisible by any prime in $\\pi$. We show that if $\\pi$ contains at most two prime numbers and the only element in $\\mathrm{Irr}_{\\pi'}(G)$ is the principal character, then $G=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09609","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"}