{"paper":{"title":"The existence of pronormal $\\pi$-Hall subgroups in $E_\\pi$-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"D.O. Revin, E.P. Vdovin","submitted_at":"2015-04-11T04:34:33Z","abstract_excerpt":"A subgroup $H$ of a group $G$ is called {\\it pronormal}, if for every $g\\in G$ subgroups $H$ and $H^g$ are conjugate in $\\langle H, H^g\\rangle$. It is proven that if a finite group $G$ possesses a $\\pi$-Hall subgroup for a set of primes $\\pi$, the every its normal subgroup (in particular, $G$ itself) possesses a $\\pi$-Hall subgroup that is pronormal in~$G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02834","kind":"arxiv","version":2},"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"}