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Math Help - groups of permutations

  1. #1
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    groups of permutations

    Let pi is a cycle in S(n) of length r. Prove that ord(pi) = r.
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  2. #2
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    Quote Originally Posted by anncar View Post
    Let pi is a cycle in S(n) of length r. Prove that ord(pi) = r.
    It is quite stairtforward. Let \pi  = (1,2,3) in S_5 for example. Not if you compose \pi with itself 3 times each element goes to itself. This happens to be its order.
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    hi, could you explain it more thoroughly?..like- what everything means? thanks.
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  4. #4
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    Quote Originally Posted by anncar View Post
    hi, could you explain it more thoroughly?..like- what everything means? thanks.
    TPH meant that if you take any element \pi \in S_n of length r, and if you compose \pi r times, that is, \underbrace{\pi \pi ... \pi}_{r \, times}, then you will get (1), the identity.. hence, the order is r..
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