Let H be a normal subgroup of finite group G. If the order of the quotient groups $\displaystyle G/H$ is m, prove that $\displaystyle g^m$ is in H for all $\displaystyle g \in G$.

So since H is normal, there are no distinctions between left and right cosets in G.

G is a finite group. Let o(G) = n. The o(G/H) = m.

Don't know where to go after this...