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Math Help - order of a permutation

  1. #1
    Junior Member
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    order of a permutation

    Find the order of g,

    S7= Sym(7)=Symmetric group 7

    G = S7, g = (1 3 5)(2 4 6 7).

    My answer is ord(g) = 12

    I know you suppose to find the lowest common multiple to find the order.. but what Im not sure about is:

    If g was not disjoint
    do you multiply together and then find its order or can you find the order the way its given.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Dreamer78692 View Post
    Find the order of g,

    S7= Sym(7)=Symmetric group 7

    G = S7, g = (1 3 5)(2 4 6 7).

    My answer is ord(g) = 12

    I know you suppose to find the lowest common multiple to find the order.. but what Im not sure about is:

    If g was not disjoint
    do you multiply together and then find its order or can you find the order the way its given.
    Good question!

    The answer, however, is no. Remember that the set of 2-cycles generates the group S_n, and so if it were true then every element would have order 2.

    For example, (12)(23) = (132). lcm(2, 2)=2 but the order of (132) is 3. So there is your counter-example.
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