if H is a normal subgroup of G and has index n, show that g^n is in H for all g in G.
The Attempt at a Solution
Take H a normal subgroup of a group G. Take g in G.
Consider gH in the quotient group G/H. Because |G/H| = [G] = n, (gH)^n = eH.
But g^nH = (gH)^n = eH. Thus g^n is in H.
please tell me if this is right or what i need to add,, thanks for your help!