{"paper":{"title":"Groups satisfying the two-prime hypothesis with a composition factor isomorphic to ${\\rm PSL}_2(q)$ for $q\\geq 7$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Hung P. Tong-Viet, Mark L. Lewis, Yanjun Liu","submitted_at":"2017-01-19T16:02:50Z","abstract_excerpt":"Let $G$ be a finite group, and write ${\\rm cd}(G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the {\\it two-prime hypothesis} if, for any distinct degrees $a, b \\in {\\rm cd}(G)$, the total number of (not necessarily different) primes of the greatest common divisor ${\\rm gcd}(a, b)$ is at most $2$. In this paper, we prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to ${\\rm PSL}_2 (q)$ for $q \\geq 7$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05490","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"}