Congruence solvability in finite Moufang loops of order coprime to three (Q6595835)

In this paper, the authors prove that a normal subloop \(X\) of a Moufang loop \(Q\) induces an abelian congruence of \(Q\) if and only if \(u(xy) = (uy)x\) for all \(x, y \in X\) and for all \(u\in Q\). Then they prove that the notions of classical solvability and congruence solvability coincide in finite \(3\)-divisible Moufang loops.