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Math Help - order of permutation

  1. #1
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    order of permutation

    let f=(x_1, x_2,...,x_r) belongs to permutation S_n. show that order of f =r.

    How to prove it?
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  2. #2
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    The thing here is to note that if you compose (x_1,...,x_r), r+1 times then x_i returns back to its own position. And this happens to be the smallest such number. Thus, (x_1,...,x_r)^{r+1} = (x_1,...,x_r) thus canceling both sides we get (x_1,...,x_r)^r = \text{Id}.
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  3. #3
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    thanks

    You make it looks so easy
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