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Math Help - group permutations 1

  1. #1
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    group permutations 1

    Find the parity of each permutation:

    b) (1 2 3 4 5 6)(7 8 9)
    c) (1 2 3 4 5 6)(1 2 3 4 5 7)
    d) (1 2)(1 2 3)(4 5)(5 6 8)(1 7 9)

    Please show steps. Thanks!
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  2. #2
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    Quote Originally Posted by mpryal View Post
    Find the parity of each permutation:

    b) (1 2 3 4 5 6)(7 8 9)
    c) (1 2 3 4 5 6)(1 2 3 4 5 7)
    d) (1 2)(1 2 3)(4 5)(5 6 8)(1 7 9)
    I do the first one you do the other ones.

    Notice, (123456) = (16)(15)(14)(13)(12) and (789)=(79)(78).
    Thus,
    (123456)(789) = (16)(15)(14)(13)(12)(79)(78).

    Notice there are 7 transpositions, so it is an odd permutation.
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