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Let a and b belong to Sn. Prove that (a^-1)(b^-1)(a)(b) is an even permutation.

  1. Feb 14, 2008 #1
    1. The problem statement, all variables and given/known data
    Let a and b belong to Sn. Prove that (a^-1)(b^-1)(a)(b) is an even permutation.


    2. Relevant equations
    Definitions I have are
    Every permutation in Sn, n>1 is a product of 2 cycles
    and
    A permutation that can be expressed as a product of an even number of 2 cycles is called an even permutation

    Thanks
     
  2. jcsd
  3. Feb 14, 2008 #2

    HallsofIvy

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    So, it appears you are saying that all the permutations involved in [itex]a^{-1}b^{-1}ab[/itex] is a two-cycle and this is a product of 4 of them!
     
  4. Feb 16, 2008 #3
    Maybe its my flu...but what do you mean exactly? What I said are two definitions out of the book.

    Do I have to show that a^-1b^-1 is one cycle and that ab is another cycle?
     
  5. Feb 16, 2008 #4

    AKG

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    If a can be expressed as a product of k 2-cycles, what can you say about how many 2-cycles it takes to express a-1?
     
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