There is a "natural" surjective group homomorphism π : G -> G/N, sending each element g of G in the coset of N to which it belongs, that is: π(g) = gN. The application π is sometimes called canonical projection. |
There is a "natural" surjective group homomorphism π : G -> G/N, sending each element g of G in the coset of N to which it belongs, that is: π(g) = gN. The application π is sometimes called canonical projection.
When G/N is finite, its order is equal to [G:N], the index of N in G.
Trivially, G/G is isomorphic to the group of order 1, and G/{1} is isomorphic to G.