{"paper":{"title":"Flag-transitive $4$-designs and $PSL(2,q)$ groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huili Dong","submitted_at":"2019-08-02T08:52:20Z","abstract_excerpt":"This paper considers flag-transitive $4$-$(q+1,k,\\lambda)$ designs with $\\lambda\\geq5$ and $q+1>k>4$. Let the automorphism group of a design $\\cal D$ be a simple group $G=PSL(2,q)$. Depend on the fact that the setwise stabilizer $G_B$ must be one of twelve kinds of subgroups, up to isomorphism we get the following two results. (i) If $10\\geq \\lambda \\geq 5$, then except $(G,G_x,G_B,k,\\lambda)=(PSL(2,761),{E_{761}}\\rtimes {C_{380}},S_4,24,7)$ or $(PSL(2,512),{E_{512}}\\rtimes {C_{511}},{D_{18}},18,8)$ undecided, $\\cal D$ is a $4$-$(24,8,5)$, $4$-$(9,8,5)$, $4$-$(8,6,6)$, $4$-$(10,9,6)$, $4$-$(9,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00760","kind":"arxiv","version":3},"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/1908.00760/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"}