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Conjugacy Groups of A5

  1. Mar 18, 2009 #1
    1. The problem statement, all variables and given/known data
    I am interested in proving that A5 has no normal subgroups except itself and {e}.

    3. The attempt at a solution
    Some proofs that I have seen use centralizers to do this, but since I haven't gone through that yet I think there should be some say to do it without them.

    My approach would be to find the conjugacy classes of A5 and use their orders to show that there cannot be a normal subgroup in A5 since a normal subgroup is a union of conjugate classes.
    But my main problem is how I should go about finding the conjugacy classes.

    Thanks for your help.
  2. jcsd
  3. Mar 19, 2009 #2

    matt grime

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    Science Advisor
    Homework Helper

    There is an identical thread to this in this forum. The advice there is: do you know the conjugacy classes of elements in S_5?
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