{"paper":{"title":"Oriented Steiner quasigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Izabella Stuhl","submitted_at":"2014-02-19T12:39:08Z","abstract_excerpt":"We introduce the notion of an oriented Steiner quasigroup and develop elements of a relevant algebraic apparatus. The approach is based upon (modified) Schreier-type $f$-extensions for quasigroups (cf. earlier works \\cite{S, NSt, NSt2}) achieved through oriented Steiner triple systems. This is done in a fashion similar to in \\cite{SS} where an analogous construction was established for loops. As a justification of this concept briefly discuss an application of oriented Steiner triple systems in cryptography using oriented Steiner quasigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4644","kind":"arxiv","version":2},"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"}