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Math Help - group permutations 6

  1. #1
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    group permutations 6

    If n >= 3, show that every element in An is a product of 3-cycles.

    Please show steps. Thanks!
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  2. #2
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    Quote Originally Posted by mpryal View Post
    If n >= 3, show that every element in An is a product of 3-cycles.

    Please show steps. Thanks!
    Pair the transpositions together. Each pair has one of each possible forms: (12)(12),(12)(23),(12)(34). Notice that (12)(12) = (123)(123)(123), (12)(23) = (123), and (12)(34) = (123)(234). Thus, altogether each permutation in A_n is a product of 3-cycles.
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