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Prove that if $P$ is a $p$-Sylow of $G$ and $N \triangleleft\> G$ then:

  1. $ PN/N $ is q $p$-Sylow of $G/N$

  2. $P \cap N $ is $p$-Sylow of $N$

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if you don't really improve your accept rate chances are not much people will be wanting to help you... –  DonAntonio Sep 4 '12 at 9:57
    
After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark ✓ next to it. This scores points for you and for the person who answered your question. If you don't do this, people are less likely to answer your later questions. –  MJD Sep 4 '12 at 10:12

1 Answer 1

up vote 2 down vote accepted

Better than writing this out, you better read this excellent expository paper by Keith Conrad, Corollary 7.5 and Theorem 7.7.

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