{"paper":{"title":"On some Frobenius groups with the same prime graph as the almost simple group PGL(2,49)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ali Mahmoudifar","submitted_at":"2016-01-02T07:01:57Z","abstract_excerpt":"The prime graph of a finite group $G$ is denoted by $\\ga(G)$ whose vertex set is $\\pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $\\ga(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $\\ga(H)=\\ga(G)$, in while $H\\not\\cong G$. In this paper, we consider finite groups with the same prime graph as the almost simple group $\\textrm{PGL}(2,49)$. Moreover, we construct some Frobenius groups whose their prime graph coincide with $\\ga(\\textrm{PGL}(2,49))$, in particular, we get that $\\textrm{PGL}(2,49"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00146","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"}