{"paper":{"title":"Cyclic extensions of Moufang loops induced by semi-automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Stephen M. Gagola III","submitted_at":"2013-06-26T14:35:09Z","abstract_excerpt":"It is well known that if a group G factorizes as G = NH where H\\leq G and N is normal in G then the group structure of G is determined by the subgroups H and N, the intersection of N with H and how H acts on N with a homomorphism f : H -> Aut(N). Here we generalize the idea by creating extensions using the semi-automorphism group of N. We show that if G=NH is a Moufang loop, N is a normal subloop, and H=<u> is a finite cyclic group of order coprime to three then the binary operation of G depends only on the binary operation of N, the intersection of N with H, and how u permutes the elements of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6261","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"}