{"paper":{"title":"On the intersections of solvable Hall subgroups in finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"E.P. Vdovin, V.I. Zenkov","submitted_at":"2008-12-17T04:44:38Z","abstract_excerpt":"In the paper we consider the following conjecture: if a finite group $G$ possesses a solvable $\\pi$-Hall subgroup $H$, then there exist elements $x,y,z,t\\in G$ such that the identity $H\\cap H^x\\cap H^y\\cap H^z\\cap H^t=O_\\pi(G)$ holds. The minimal counter example is shown to be an almost simple group of Lie type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3204","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"}