{"paper":{"title":"Number of Sylow subgroups in finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Evgeny Vdovin, Wenbin Guo","submitted_at":"2017-09-01T04:09:05Z","abstract_excerpt":"Denote by $\\nu_p(G)$ the number of Sylow $p$-subgroups of $G$. It is not difficult to see that $\\nu_p(H)\\leq\\nu_p(G)$ for $H\\leq G$, however $\\nu_p(H)$ does not divide $\\nu_p(G)$ in general. In this paper we reduce the question whether $\\nu_p(H)$ divides $\\nu_p(G)$ for every $H\\leq G$ to almost simple groups. This result substantially generalizes the previous result by G. Navarro and also provides an alternative proof for the Navarro theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00148","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"}