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.

http://img14.imageshack.us/img14/665...10301at819.png

I have now been asked to prove this:

http://img824.imageshack.us/img824/6...10301at819.png

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.

Quote:

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Originally Posted by CropDuster

So this is what I have been asked to prove, and I have included my proof.

http://img14.imageshack.us/img14/665...10301at819.png

I have now been asked to prove this:

http://img824.imageshack.us/img824/6...10301at819.png

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.

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

Tonio