{"paper":{"title":"The influence of $\\mathfrak{F_{\\mathrm s}}$-quasinormality of subgroups on the structure of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Wenbin Guo, Xiaolong Yu, Xiaoyu Chen","submitted_at":"2014-01-22T05:49:51Z","abstract_excerpt":"Let $\\frak{F}$ be a class of finite groups. A subgroup $H$ of a finite group $G$ is said to be $\\mathfrak{F_{\\mathrm s}}$-quasinormal in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is $s$-permutable in $G$ and $(H\\cap T)H_G/H_G$ is contained in the $\\frak{F}$-hypercenter $Z_\\infty^\\mathfrak{F}(G/H_G)$ of $G/H_G$. In this paper, we investigate further the influence of $\\mathfrak{F_{\\mathrm s}}$-quasinormality of some subgroups on the structure of finite groups. New characterization of some classes of finite groups are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5560","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"}