{"paper":{"title":"Inclusions of innately transitive groups into wreath products in product action with applications to $2$-arc-transitive graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Cai-Heng Li, Cheryl E. Praeger, Csaba Schneider","submitted_at":"2015-07-03T23:58:43Z","abstract_excerpt":"We study $(G,2)$-arc-transitive graphs for innately transitive permutation groups $G$ such that $G$ can be embedded into a wreath product $\\sym\\Gamma\\wr\\sy\\ell$ acting in product action on $\\Gamma^\\ell$. We find two such connected graphs: the first is Sylvester's double six graph with 36 vertices, while the second is a graph with $120^2$ vertices whose automorphism group is $\\aut\\sp 44$. We prove that under certain conditions no more such graphs exist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01049","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"}