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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1110.1308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-06T16:02:29Z","cross_cats_sorted":[],"title_canon_sha256":"8f8279ff3dc611fbe4bf40589dc9f74ad9b3ddadb85c4051da993f573f33f652","abstract_canon_sha256":"ba53f642da49280edf213d947313dbdee4b0a8c675b8ff7c2917ea95de09065e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:32.305875Z","signature_b64":"vqf+f+ABTy9RTcTlN67yrys6PBgwjubm4jtvMCbQIWGnXC3nxcsOuzV4bR5dYeo+Zo9ZU/rF3qq7o7eWh/dbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ea2c708df87e2b9d015a19272cf81b04a12adeec261d3e23a47a3632f773ba0","last_reissued_at":"2026-05-18T04:11:32.305324Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:32.305324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $z \\in Z(S)$. 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