1. The problem statement, all variables and given/known data Prove that if p is a prime and G is a group of order p^a for some a in Z+, then every subgroup of index p is normal in G. 2. Relevant equations We know the order of H is p^(a-1). H is a maximal subgroup, if that matters. 3. The attempt at a solution Suppose H≤G and (G)=p but H is not a normal subgroup of G. So for some g in G Hg≠gH. I know I didn't do much, but is this the correct way to start? What to do now?