Prove that no group of order pq,where p and q are both prime, is simple.
So this is what I have been asked to prove, and I have included my proof.
I have now been asked to prove this:
I feel like the proof for this is exactly the same as the previous proof. Am I missing something? It seems too easy. I think I can use the exact same argument to show that and that therefore the Sylow q-subgroup is normal.