engleski

Finite hexagonal quasigroups

Hexagonal quasigroups are idempotent, medial and semisymmetric quasigroups. Some basic examples are given, and products and subquasigroups of hexagonal quasigroups are discussed. Commutative hexagonal quasigroups are classified, and hexagonal quasigroups generated by cyclic groups are explored. It is known that a hexagonal quasigroup can be obtained from any Abelian group G allowing automorphism $\phi$ such that for all $x\in G$, $\phi\circ\phi(x) - \phi(x) + x = 0$. It is proven that such an automorphism exists on certain subgroups of such group G, also. Finally, the question of possible orders of the hexagonal quasigroups is answered.

quasigroup

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