{"paper":{"title":"Block-transitive and point-primitive $2$-$(v,k,2)$ designs with sporadic socle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Shenglin Zhou, Xiaohong Zhang","submitted_at":"2016-03-24T01:19:25Z","abstract_excerpt":"The purpose of this paper is to classify all pairs $(\\mathcal{D}, G)$, where $\\mathcal{D}$ is a non-trivial $2$-$(v, k, 2)$ design, and $G\\leq Aut(\\mathcal{D})$ acts transitively on the set of blocks of $\\mathcal{D}$ and primitively on the set of points of $\\mathcal{D}$ with sporadic socle. We prove that there exists only one such pair $(\\mathcal{D}, G)$ in which $\\mathcal{D}$ is a $2$-$(176,8,2)$ design and $G=HS$, the Higman-Sims simple group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07405","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"}