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 \(u(xy) = (uy)x\) $u(xy)=(uy)x$ for all \(x,y\in X\) $x,y\in X$ and \(u\in Q\) $u\in Q$ . This characterization is then used to show that classically solvable finite 3-divisible Moufang loops are congruence solvable.