{"paper":{"title":"On the $\\pi$$\\mathfrak{F}$-norm and the $\\mathfrak{H}$-$\\mathfrak{F}$-norm of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Wenbin Guo, Xiaoyu Chen","submitted_at":"2013-08-05T11:44:34Z","abstract_excerpt":"Let $\\mathfrak{H}$ be a Fitting class and $\\mathfrak{F}$ a formation. We call a subgroup $\\mathcal{N}_{\\mathfrak{H},\\mathfrak{F}}(G)$ of a finite group $G$ the $\\mathfrak{H}$-$\\mathfrak{F}$-norm of $G$ if $\\mathcal{N}_{\\mathfrak{H},\\mathfrak{F}}(G)$ is the intersection of the normalizers of the products of the $\\mathfrak{F}$-residuals of all subgroups of $G$ and the $\\mathfrak{H}$-radical of $G$. Let $\\pi$ denote a set of primes and let $\\mathfrak{G}_\\pi$ denote the class of all finite $\\pi$-groups. We call the subgroup $\\mathcal{N}_{\\mathfrak{G}_\\pi,\\mathfrak{F}}(G)$ of $G$ the $\\pi\\mathfrak{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0948","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"}