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Homework Help: Conjugacy classes in an

  1. Mar 1, 2010 #1
    (Moderator's note: thread moved from "Set Theory, Logic, Probability, Statistics")

    the question is
    if n is odd then there are exactly two conjugacy classes of n cycles in An each of which contains (n-1)!/2 elements.
    also there is a hint says let An act on itself
    i know the fact that since An acts on itself, x doesnt commute with any odd permutation. So it splits into two Ccl An (x) and CCl An (12)x(12).
    But i cant figure it out how to calculate either the number of stabilizers or the number of orbits
     
    Last edited by a moderator: Mar 3, 2010
  2. jcsd
  3. Mar 2, 2010 #2
    Your question is rather difficult to understand. eg. what do you mean by "CCl", "Ccl", (12)x(12)? And what is x?

    I don't even think this is true! eg: in A3, the two 3-cycles: (123) and (132) commute, and so they are in the same conjugacy class.

    For what it's worth, it might help you to note that if n is odd, then An contains every n-cycle, as these are even permutations. Also that the number of these n-cycles is: (n-1)! (as we can fix the 1 at the beginning of the cycle and then permute the other (n-1) numbers in every possible way).

    Otherwise you will need to explain more.
     
  4. Mar 2, 2010 #3
    well the permutations you gave they are in ccl An
    its what is written on my lecture notes actually i also dont know much about it but it has the same conj. class with ccl an
     
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