medial quasigroup

A medial quasigroup is a quasigroupPlanetmathPlanetmath such that, for any choice of four elements a,b,c,d, one has


Any commutativePlanetmathPlanetmathPlanetmath quasigroup is trivially a medial quasigroup. A nontrivial class of examples may be constructed as follows. Take a commutative group (G,+) and two automorphismsPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath f,g:GG which commute with each other, and an element c of G. Then, if we define an operationMathworldPlanetmath :G×GG as


(G,) is a medial quasigroup.


V. D. Belousov, Fundamentals of the theory of quasigroups and loops (in Russian)

Title medial quasigroup
Canonical name MedialQuasigroup
Date of creation 2013-03-22 16:27:33
Last modified on 2013-03-22 16:27:33
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 5
Author rspuzio (6075)
Entry type Definition
Classification msc 20N05