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Math Help - Orders of permutations

  1. #1
    Junior Member universalsandbox's Avatar
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    Orders of permutations

    What is the order of a permutation telling you about it?
    And how to find the following orders

    (1 5 4)(2 3 7)(6 8)
    (1 3 5 7)(2 6)(4 8)

    Thanks!
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  2. #2
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    Quote Originally Posted by universalsandbox View Post
    What is the order of a permutation telling you about it?
    And how to find the following orders

    (1 5 4)(2 3 7)(6 8)
    (1 3 5 7)(2 6)(4 8)

    Thanks!
    Since these are disjoint cycles the order is the lcm of their lengths.
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  3. #3
    Junior Member universalsandbox's Avatar
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    so how would you find the length of a cycle?
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    Quote Originally Posted by universalsandbox View Post
    so how would you find the length of a cycle?
    The length of (1 5 4) is 3.
    The length of (237) is 3.
    The length of (68) is 2.

    Find \text{lcm}(3,3,2) = 6.
    And that is the order.
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