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 \(Q\).
scientific article; zbMATH DE number 2119245