Given a group *G* and a normal subgroup *N* there is a natural way to
associate elements of the group with the factor group in such a way as to
give a homomorphism. This mapping is and is called the
*natural homomomorphism*. It is of course onto and so an epimorphism.
The kernel of the map is *N*. Any two elements of *G* that are in the same
coset of *N* in *G* are mapped to the same element of the factor group.

Sun Mar 30 14:48:35 PST 1997