{"paper":{"title":"On one generalization of modular subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bin Hu, Jianhong Huang, Xun Zheng","submitted_at":"2017-08-11T14:15:50Z","abstract_excerpt":"Let $G$ be a finite group.\n  If $M_n < M_{n-1} < \\ldots < M_1 < M_{0}=G $ where $M_i$ is a maximal subgroup of $M_{i-1}$ for all $i=1, \\ldots ,n$, then $M_n $ ($n > 0$) is an \\emph{$n$-maximal subgroup} of $G$.\n  A subgroup $M$ of $G$ is called \\emph{modular} if the following conditions are held: (i) $\\langle X, M \\cap Z \\rangle=\\langle X, M \\rangle \\cap Z$ for all $X \\leq G, Z \\leq G$ such that $X \\leq Z$, and (ii) $\\langle M, Y \\cap Z \\rangle=\\langle M, Y \\rangle \\cap Z$ for all $Y \\leq G, Z \\leq G$ such that $M \\leq Z$.\n  In this paper, we study finite groups whose $n$-maximal subgroups are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03550","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"}