Thread: 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.

Originally Posted by CropDuster

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.

No, it's not exactly the same: this time it may be , which
it's easily possible.

Tonio