A variety of Steiner loops satisfying Moufang's theorem: a solution to Rajah's Problem.

A loop X is said to satisfy Moufang's theorem if for every x , y , z ∈ X such that x (y z) = (x y) z the subloop generated by x, y, z is a group. We prove that the variety V of Steiner loops satisfying the identity (x z) (((x y) z) (y z)) = ((x z) ((x y) z)) (y z) is not contained in the variety of Moufang loops, yet every loop in V satisfies Moufang's theorem. This solves a problem posed by Andrew Rajah. [ABSTRACT FROM AUTHOR]