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Math Help - cycle

  1. #1
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    cycle

    Express the following permutations as the product of transpositions:

    a) (1 2 3 5 7)(2 4 7 6)
    b) (1 2)(1 3)(1 4)
    e) (1 2 3)(3 5 7 9)(1 2 3)^-1
    f) (1 2 3 4 5)^3.


    Please show steps. Thanks!
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  2. #2
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    Quote Originally Posted by mpryal View Post
    Express the following permutations as the product of transpositions:

    a) (1 2 3 5 7)(2 4 7 6)
    b) (1 2)(1 3)(1 4)
    e) (1 2 3)(3 5 7 9)(1 2 3)^-1
    f) (1 2 3 4 5)^3.


    Please show steps. Thanks!
    Same approach at has down here.

    You just need to know that (a_1,a_2,...,a_k) = (a_1,a_k)...(a_1,a_3)(a_1, a_2)

    Also that (a_1,a_2,...,a_k)^{-1} = [(a_1,a_k)...(a_1,a_3)(a_1, a_2)]^{-1} = (a_1,a_2)(a_1,a_3)....(a_1,a_k)

    And for (12345)^3 just imagine (12345)(12345)(12345).

    Show you work.
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