The Moufang theorem for all analytic loops from a non-Moufang variety of loops

摘要

A loop Q satisfies the Moufang theorem if Q possesses the following property: let be associate, that is then x, y, z generate a subgroup of Q. It remains an open problem in the theory of loops to find a non-Moufang variety of loops satisfying the Moufang Theorem. We describe the non-Moufang varieties B-n of diassociative loops such that all analytic loops from B-n satisfy the above mentioned property.