{"paper":{"title":"On $H_{\\sigma}$-permutably embedded and $H_{\\sigma}$-subnormaly embedded subgroups of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander N. Skiba, Chi Zhang, Darya A. Sinitsa, Wenbin Guo","submitted_at":"2017-01-18T16:27:43Z","abstract_excerpt":"Let $G$ be a finite group. Let $\\sigma =\\{\\sigma_{i} | i\\in I\\}$ be a partition of the set of all primes $\\Bbb{P}$ and $n$ an integer. We write $\\sigma (n) =\\{\\sigma_{i} |\\sigma_{i}\\cap \\pi (n)\\ne \\emptyset \\}$, $\\sigma (G) =\\sigma (|G|)$. A set $ {\\cal H}$ of subgroups of $G$ is said to be a complete Hall $\\sigma $-set of $G$ if every member of ${\\cal H}\\setminus \\{1\\}$ is a Hall $\\sigma_{i}$-subgroup of $G$ for some $\\sigma_{i}$ and ${\\cal H}$ contains exact one Hall $\\sigma_{i}$-subgroup of $G$ for every $\\sigma_{i}\\in \\sigma (G)$. A subgroup $A$ of $G$ is called: (i) a $\\sigma$-Hall subgro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05134","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"}