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Normal subgroup question

  1. May 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Show that if G is a group of order 168 that has a normal subgroup of order 4, then G has a normal subgroup of order 28.


    2. Relevant equations



    3. The attempt at a solution
    Let H be a normal subgroup of order 4. Then |G/H|=42=2*3*7, so then G?N has a unique, and therefore normal Sylow 7-subgroup, lets call it K.
    I was told to use the correspondence theorem, but I am not sure where it works in here. any ideas?
     
  2. jcsd
  3. May 13, 2010 #2

    jbunniii

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    Why don't you start by stating what the correspondence theorem says? The result you are seeking is an immediate consequence.
     
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