Congruence Solvability in Finite Moufang Loops of Order Coprime to Three.

We prove that a normal subloop X of a Moufang loop Q induces an abelian congruence of Q if and only if u (x y) = (u y) x for all x , y ∈ X and u ∈ Q . This characterization is then used to show that classically solvable finite 3-divisible Moufang loops are congruence solvable. [ABSTRACT FROM AUTHOR]