{"paper":{"title":"On weakly $sigma$-permutable subgroups of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Chi Zhang, W. Guo, Zhenfeng Wu","submitted_at":"2016-08-10T16:11:33Z","abstract_excerpt":"Let G be a finite group and {\\sigma} = {{\\sigma}_i, i \\in I} be a partition of the set of all primes \\mathbb{P}. A set \\mathcal{H} of subgroups of G with 1 \\in \\mathcal{H} 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. A subgroup H of G is said to be {\\sigma}-permutable if G possesses a complete Hall {\\sigma}-set \\mathcal{H} such that HA^x = A^xH for all A \\in \\mathcal{H} and all x \\in G. We say that a subgroup H of G is weakly {\\sigma}-permutable in G if there exists a {\\sigma}-subnormal subgroup T of G such that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03224","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"}