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Homework Help: 3-cycle or a product of three cycles permutations

  1. Sep 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Show that every element in A(n)= set of even permutations, for n> or equal to 3 can be expressed as a 3-cycle or a product of three cycles.

    2. Relevant equations
    3-cycle = (_ _ _). a permutation is a function from a set A to A that is bijective.

    3. The attempt at a solution
    for n=3 a permuation can be (1 2 3), (1 3 2), (2 1 3), (3 1 2) etc... need help for n>3
  2. jcsd
  3. Sep 26, 2010 #2


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    Staff Emeritus
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    Gold Member

    Re: permutations

    What factorization do you already know you can do to an even permutation?
  4. Sep 26, 2010 #3
    Re: permutations

    Do you mean how can you express it? You can express an even permutation into a product of even number of 2-cycles. also the order of A(n) is n!/2
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