{"paper":{"title":"Affine Extensions of loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Agota Figula, Karl Strabach","submitted_at":"2015-06-29T14:54:58Z","abstract_excerpt":"We show a simple geometric procedure for an extension of a loop realized as the image $\\Sigma ^{\\ast}$ of a sharply transitive section in a subgroup $G^{\\ast}$ of the projective linear group $PGL(n-1, \\mathbb K)$ to a loop realized as the image of a sharply transitive section in a group $\\Delta =T' \\rtimes C$ of affinities of the $n$-dimensional space ${\\cal A}_n=\\mathbb K^n$ over a commutative field $\\mathbb K$. We desire that $T'$ is a large subgroup of affine translations and that $\\alpha (C)=G^{\\ast}$ holds for the canonical homomorphism $\\alpha :GL(n,\\mathbb K) \\to PGL(n, \\mathbb K)$. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08664","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"}