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Permutation conjugation

  1. Oct 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that there is no such permutation a such that
    (a-inverse)*(1,2)*(a) = (3,4)(1,5)


    3. The attempt at a solution
    Does it have something to do with the order of (1,2)? I know the order is 2, so if we square (a-inverse)*(1,2)*(a), then we get the identity....how else can I think about it?
     
  2. jcsd
  3. Oct 30, 2008 #2

    morphism

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    Do you know anything about cycle types? In particular, can you prove that they are invariant under conjugation?

    If not, notice that 1->5 on the RHS. Convince yourself that (1,2) must send a(1) to a(5). Do the same for 3.
     
  4. Oct 30, 2008 #3
    By a(1) and a(5) do you mean the numbers 1 and 5 in whatever the permutation a is?
     
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