{"paper":{"title":"Block-transitive t-(k^2,k,\\lambda) designs associated to two dimensional projective special linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Guoqiang Xiong, Haiyan Guan","submitted_at":"2025-08-27T02:06:52Z","abstract_excerpt":"This paper investigates block-transitive automorphism groups of t-(k^2,k,\\lambda) designs. Let D be a non-trivial t-(k^2,k,\\lambda) design, G \\leq \\Aut(D) be block-transitive with X\\unlhd G\\leq \\Aut(X), where X = PSL(2,q)(q\\geq4). Then q = 8 and D is a 2-(36,6,\\lambda) design with \\lambda \\in \\{2,6,9,12,18,36\\}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.19515","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.19515/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}