{"paper":{"title":"Groups which are almost groups of Lie type in characteristic p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Chris Parker, Gernot Stroth","submitted_at":"2011-10-06T16:02:29Z","abstract_excerpt":"For a prime $p$, a $p$-subgroup of a finite group $G$ is said to be large if and only if $Q= F^*(N_G(Q))$ and, for all $1 \\neq U \\le Z(Q)$, $N_G(U) \\le N_G(Q)$. In this article we determine those groups $G$ which have a large subgroup and which in addition have a proper subgroup $H$ containing a Sylow $p$-subgroup of $G$ with $F^*(H)$ a group of Lie type in characteristic $p$ and rank at least 2 (excluding $\\PSL_3(p^a)$) and $C_H(z)$ soluble for some $z \\in Z(S)$. This work is part of a project to determine the groups $G$ which contain a large $p$-subgroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1308","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"}