(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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. -I've managed to prove it..

2. Prove that every normal p-subgroup of G is contained in Op(G) -I've managed to prove this also...

3. Let's mark: G] = G/Op(G). Prove that Op(G] ) ={1} -I have no idea about this...

Help is needed :(

Tnx

2. Relevant equations

3. The attempt at a solution

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# Abstract-Sylow Theorems

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