Frobenius Quasigroups and Regular Polygons
Copyright policy )Frobenius Quasigroups and Regular Polygons
The authors discuss in this paper which conditions force a Frobenius quasigroup to have a multiplication that is one of the geometric multiplications defined by the regular \(n\)-gons. Topological Frobenius quasigroups \(Q\) homeomorphic to a connected topological variety as well as algebraic connected Frobenius quasigroups are of this type if they have no epimorphic image with left translations of the same order as \(Q\). Beside of this they characterize properties considered in the theory of quasigroups within the Frobenius group \(G\) generated by the left translations of a Frobenius quasigroup \(Q\).
- University of Bergen Norway
Frobenius groups, Loops, quasigroups, Other topological algebraic systems and their representations, left translations, Geometries with algebraic manifold structure, Topological geometries on manifolds, left distributive quasigroups, topological Frobenius quasigroups
Frobenius groups, Loops, quasigroups, Other topological algebraic systems and their representations, left translations, Geometries with algebraic manifold structure, Topological geometries on manifolds, left distributive quasigroups, topological Frobenius quasigroups
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