{"paper":{"title":"On $\\sigma$-quasinormal 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, Bin Hu, Jianhong Huang","submitted_at":"2018-01-28T14:10:46Z","abstract_excerpt":"Let $G$ be a finite group and $\\sigma =\\{\\sigma_{i} | i\\in I\\}$ some partition of the set of all primes $\\Bbb{P}$, that is, $\\sigma =\\{\\sigma_{i} | i\\in I \\}$, where $\\Bbb{P}=\\bigcup_{i\\in I} \\sigma_{i}$ and $\\sigma_{i}\\cap \\sigma_{j}= \\emptyset $ for all $i\\ne j$. We say that $G$ is $\\sigma$-primary if $G$ is a $\\sigma _{i}$-group for some $i$. A subgroup $A$ of $G$ is said to be: ${\\sigma}$-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 $A_{i}/(A_{i-1})_{A_{i}}$ is $\\sigma$-primary for all $i=1, \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09234","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"}