{"paper":{"title":"Finite groups with systems of $K$-$\\frak{F}$-subnormal subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander N. Skiba, Vladimir N. Semenchuk","submitted_at":"2017-05-30T07:09:02Z","abstract_excerpt":"Let $\\frak {F}$ be a class of group. A subgroup $A$ of a finite group $G$ is said to be $K$-$\\mathfrak{F}$-subnormal in $G$ if there is a subgroup chain $$A=A_{0} \\leq A_{1} \\leq \\cdots \\leq A_{n}=G$$ such that either $A_{i-1} \\trianglelefteq A_{i}$ or $A_{i}/(A_{i-1})_{A_{i}} \\in \\mathfrak{F}$ for all $i=1, \\ldots , n$. A formation $\\frak {F}$ is said to be $K$-lattice provided in every finite group $G$ the set of all its $K$-$\\mathfrak{F}$-subnormal subgroups forms a sublattice of the lattice of all subgroups of $G$.\n  In this paper we consider some new applications of the theory of $K$-latt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10476","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"}