{"paper":{"title":"On the Connectivity of the Sylow Graph of a Finite Group","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Francesco G. Russo (Universita' degli Studi di Palermo, Italy), Palermo","submitted_at":"2010-02-25T19:34:27Z","abstract_excerpt":"The Sylow graph $\\Gamma(G)$ of a finite group $G$ originated from recent investigations on the so--called $\\mathbf{N}$--closed classes of groups. The connectivity of $\\Gamma(G)$ was proved only few years ago, involving the classification of finite simple groups, and the structure of $G$ may be strongly restricted, once information on $\\Gamma(G)$ are given. The first result of the present paper deals with a condition on $\\mathbf{N}$--closed classes of groups. The second result deals with a computational criterion, related to the connectivity of $\\Gamma(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4853","kind":"arxiv","version":5},"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"}