{"paper":{"title":"On p-nilpotency of finite groups?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Baojun LI, Tuval Foguel","submitted_at":"2013-08-02T05:00:47Z","abstract_excerpt":"Let $H$ be a subgroup of a group $G$. $H$ is said satisfying $\\Pi$-property in $G$, if $|G/K:N_{G/K}(HK/K\\cap L/K)|$ is a\n  $\\pi(HK/K\\cap L/K))$-number for any chief factor $L/K$ of $G$, and, if there is a subnormal supplement $T$ of $H$ in $G$ such that $H\\cap T\\le I\\le H$ for some subgroup $I$ satisfying $\\Pi$-property in $G$, then $H$ is said $\\Pi$-normal in $G$. By these properties of some subgroups, we obtain some new criterions of $p$-nilpotency of finite groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0408","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"}