1. The problem statement, all variables and given/known data if H is a normal subgroup of G and has index n, show that g^n is in H for all g in G. 3. 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!