The best known of Oaxaca's moles is mole negro, which is darker than mole poblano and just as thick and rich. It also includes chocolate, as well as chili peppers, onions, garlic and more, but what makes it distinct is the addition of a plant called hoja santa. It is the most complex and difficult to make of the sauces.
The equivalence of this definition with the earlier one is often called the subgroup condition. For full proof, refer: Sufficiency of subgroup condition. It has two forms (left and right): A subset of a group is termed a subgroup if it is nonempty and is closed under the left quotient of elements. In other words, a subset of a group is termed a subgroup if and only if is nonempty and whenever. A subset of a group is termed a subgroup if it is nonempty and is closed under the right quotient of elements.
Then is the normal subgroup generated by the set of commutators of elements of. Proof. Let be the normal subgroup generated by the commutators of elements of. By definition, . On the other hand, the set generates the group; since the elements of commute, is abelian, and hence.he group generated by the set of commutators of is called the derived group of. It is also called the commutator group of, though in general it is distinct from the set of commutators of. It is a normal subgroup of âin fact, it is a characteristic subgroup.