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Math Help - Permutation Groups...

  1. #1
    Junior Member ginafara's Avatar
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    Permutation Groups...

    Can anyone help me with this???

    Let a (alpha) and B (beta) belong to Sn. Prove that a^(-1)B^(-1)ab is an even permutation.

    I understand how this works with a specific set, but not sure how to show the general case.

    TIA
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  2. #2
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    Quote Originally Posted by ginafara View Post
    Can anyone help me with this???

    Let a (alpha) and B (beta) belong to Sn. Prove that a^(-1)B^(-1)ab is an even permutation.

    I understand how this works with a specific set, but not sure how to show the general case.

    TIA
    If "a" is even then the inverse of "a" is also even. And if "a" is odd then the inverse of "a" is odd. Similarly with "b'. So a^(-1)b^(-1)ab must be even.
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