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We prove that if $T\\trianglelefteq G\\leq Aut(T)$ where $T$ is an exceptional group of Lie type, then $T$ must be the Ree group or Suzuki group, and there are five classes of non-isomorphic designs $\\mathcal{D}$."},"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":"1907.06425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-15T10:53:12Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"20e8ba6040553e3acd4345ed6c779b0de6d85e75afda54c7e7a898ab873b3749","abstract_canon_sha256":"bd59440bdda837452c97925bac25caf191f8908fb436242f4201343e109f2327"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:37.691194Z","signature_b64":"IkybTE09etmxA0992nxNIdZyOxFUF0XS2uB0FdhPhYqBbQfo4yPWqFhVkilRNb1GijZxQpS58VqhxjUGeSJLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa288cc4bb25c1cef4fb05efcc505db22a50ec3b2e1ded72bbf9ed01e02418f3","last_reissued_at":"2026-05-17T23:40:37.690766Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:37.690766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flag-transitive non-symmetric $2$-designs with $(r,\\lambda)=1$ and exceptional groups of Lie type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Shenglin Zhou, Yongli Zhang","submitted_at":"2019-07-15T10:53:12Z","abstract_excerpt":"This paper determined all pairs $(\\mathcal{D},G)$ where $\\mathcal{D}$ is a non-symmetric 2-$(v,k,\\lambda)$ design with $(r,\\lambda)=1$ and $G$ is the almost simple flag-transitive automorphism group of $\\mathcal{D}$ with an exceptional socle of Lie type. 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