{"paper":{"title":"On the intersection of the $\\cal F$-maximal subgroups and the generalized ${\\cal F}$-hypercentre of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander N. Skiba, Wenbin Guo","submitted_at":"2012-05-11T12:21:50Z","abstract_excerpt":"Let $\\cal F$ be a class of groups. A chief factor $H/K$ of a group $G$ is called \\emph{${\\cal F}$-central in $G$} provided $(H/K)\\rtimes (G/C_{G}(H/K)) \\in {\\cal F}$. We write $Z_{\\pi{\\cal F}}(G)$ to denote the product of all normal subgroups of $G$ whose $G$-chief factors of order divisible by at least one prime in $\\pi$ are $\\cal F$-central. We call $Z_{\\pi{\\cal F}}(G)$ the $\\pi{\\cal F}$-hypercentre of $G$. A subgroup $U$ of a group $G$ is called \\emph{$\\cal F$-maximal} in $G$ provided that (a) $U\\in {\\cal F}$, and (b) if $U\\leq V\\leq G$ and $V\\in {\\cal F}$, then $U=V$.\n  In this paper we st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2498","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"}