{"paper":{"title":"On The Unrecognizability by Prime Graph for the Most Simple Group ${\\rm {\\bf PGL(2,9)}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ali Mahmoudifar","submitted_at":"2016-01-08T15:02:14Z","abstract_excerpt":"The prime graph of a finite group $G$ is denoted by $\\ga(G)$. Also $G$ is called recognizable by prime graph if and only if each finite group $H$ with $\\ga(H)=\\ga(G)$, is isomorphic to $G$. In this paper, we classify all finite groups with the same prime graph as $\\textrm{PGL}(2,9)$. In particular, we present some solvable groups with the same prime graph as $\\textrm{PGL}(2,9)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01894","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"}