{"paper":{"title":"Some computational results on small 3-nets embedded in a projective plane over a field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gabor P. Nagy, Nicola Pace","submitted_at":"2011-08-17T06:56:33Z","abstract_excerpt":"In this paper, we investigate dual 3-nets realizing the groups $C_3 \\times C_3$, $C_2 \\times C_4$, $\\Alt_4$ and that can be embedded in a projective plane $PG(2,\\mathbb K)$, where $\\mathbb K$ is an algebraically closed field. We give a symbolically verifiable computational proof that every dual 3-net realizing the groups $C_3 \\times C_3$ and $C_2 \\times C_4$ is algebraic, namely, that its points lie on a plane cubic. Moreover, we present two computer programs whose calculations show that the group $\\Alt_4$ cannot be realized if the characteristic of $\\mathbb K$ is zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3408","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"}