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December 14th, 2009, 04:03 AM   #1
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P-Sylow groups

Hey there,

Help is needed in the next question:

Let G be a finite group of order n and let p be a prime number that divides n.
Let's mark as Op(G) as the intersection of all p-sylow groups of G.

1. Prove that Op(G) is a normal p-subgroup in G.-Proved it
2. Prove that every normal p-subgroup of G is contained in Op(G)-Proved it
Can't understand how to prove this one:
3. Let's mark: G] = G/Op(G). Prove that Op(G] ) ={1}


TNX everyone!
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