{"paper":{"title":"On an open problem of Skiba","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Chi Zhang, Wenbin Guo, Zhenfeng Wu","submitted_at":"2018-05-14T10:13:40Z","abstract_excerpt":"Let $\\sigma=\\{\\sigma_{i}|i\\in I\\}$ be some partition of the set $\\mathbb{P}$ of all primes, that is, $\\mathbb{P}=\\bigcup_{i\\in I}\\sigma_{i}$ and $\\sigma_{i}\\cap \\sigma_{j}=\\emptyset$ for all $i\\neq j$. Let $G$ be a finite group. A set $\\mathcal {H}$ of subgroups of $G$ is said to be a complete Hall $\\sigma$-set of $G$ if every non-identity member of $\\mathcal {H}$ is a Hall $\\sigma_{i}$-subgroup of $G$ and $\\mathcal {H}$ contains exactly one Hall $\\sigma_{i}$-subgroup of $G$ for every $\\sigma_{i}\\in \\sigma(G)$. $G$ is said to be a $\\sigma$-group if it possesses a complete Hall $\\sigma$-set. A "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05097","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"}