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Natural homomorphism

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 tex2html_wrap_inline1925 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.

Peter Williams
Sun Mar 30 14:48:35 PST 1997