{"paper":{"title":"Finite groups with permutable Hall subgroups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Nanying Yang, Xia Yin","submitted_at":"2017-02-11T02:03:03Z","abstract_excerpt":"Let $\\sigma =\\{\\sigma_{i} | i\\in I\\}$ be a partition of the set of all primes $\\Bbb{P}$ and $G$ a finite group. A set ${\\cal H}$ of subgroups of $G$ is said to be a \\emph{complete Hall $\\sigma $-set} of $G$ if every member $\\ne 1$ of ${\\cal H}$ is a Hall $\\sigma _{i}$-subgroup of $G$ for some $i\\in I$ and $\\cal H$ contains exactly one Hall $\\sigma _{i}$-subgroup of $G$ for every $i$ such that $\\sigma _{i}\\cap \\pi (G)\\ne \\emptyset$. In this paper, we study the structure of $G$ assuming that some subgroups of $G$ permutes with all members of ${\\cal H}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03371","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"}