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Math Help - write (12345) as product of 3 cycles

  1. #1
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    write (12345) as product of 3 cycles

    Hi,

    I need help on how to write (12345) as product of 3-cycles. Any suggestion?

    Thank you.
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  2. #2
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    Quote Originally Posted by nguy0688 View Post
    I need help on how to write (12345) as product of 3-cycles.
    Do you know how to express (12345) as a product of transpositions? If so, just pair off the transpositions to form 3-cycles.

    More specifically, (12345) = (15)(14)(13)(12). The product (15)(14) is a 3-cycle, and so is (13)(12).
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  3. #3
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    Try to show something stronger: every even permutation on n>2 letters is a product of 3-cycles.
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