Abelian congruences and solvability in Moufang loops

In groups, an abelian normal subgroup induces congruence. We construct a class of centrally nilpotent Moufang loops containing subloop that does not induce On the other hand, we prove in 6-divisible loops, every congruence solvability adopted from universal-algebraic commutator theory modular varieties is strictly stronger than classical group theory. It open problem whether two notions coincide loops. they and odd order. fact, show loop order solvable, thus strengthening Glauberman's Odd Order Theorem for