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Math Help - Find the no. of distinct left cosets of H = { e, (16), (23), (16)(23)} in H6.

  1. #1
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    Find the no. of distinct left cosets of H = { e, (16), (23), (16)(23)} in H6.

    Hi anyone knows how to solve this?

    find the number of distinct left cosets of H ={e, (16), (23), (16)(23)} in H6?

    My workings as below,
    Since H6, 6!= 1x2x3x4x5x6=720
    Since H has 4 elements, i take 720/4=180 (Answer)

    Please correct me if i am wrong.

    Thanks.
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  2. #2
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    Re: Find the no. of distinct left cosets of H = { e, (16), (23), (16)(23)} in H6.

    By H6, I assume you mean the symmetric group on 6 elements. I've seen that denoted S_6 or Sym\{1, 2,...,6\}, but never H_6.
    With that assumption, your reasoning and answer are correct.
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