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    Order of a Permutation

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    Find the order of sigma^1000, where sigma is the permutation (123456789)
    (378945216)

    Find the order of , where is the permutation .

    Solution. Since and . Let , we have

    where k, m and n are positive integers.

    So,

    So, the order of is 3.

    I got this solution but I don't understand why the permutation raised to the 1000 power=(138). Why do the other elements just map to themselves? Can you elaborate on this anymore. Also why is it necessary to put 1000= 333*3+1 = 500 * 2 = 250 * 4.

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    https://brainmass.com/math/combinatorics/order-permutation-11928

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    Find the order of , where is the permutation .

    Solution. Since and . Let , we have

    where k, m and n are positive integers.

    So,

    So, the order of is 3.

    I got this solution but I don't understand why the permutation raised to the 1000 ...

    Solution Summary

    The order of a permutation is found. The solution is detailed and well presented.

    $2.19

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