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Math Help - normal subgroup

  1. #1
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    normal subgroup

    If H is a subgroup of a finite group G of index [G: H] two, then H is normal in G.
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  2. #2
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    Quote Originally Posted by apple2009 View Post
    If H is a subgroup of a finite group G of index [G: H] two, then H is normal in G.
    Hint - What can you say about right and left cosets of H? And, hence about H.
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  3. #3
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    Quote Originally Posted by aman_cc View Post
    Hint - What can you say about right and left cosets of H? And, hence about H.
    To prove for normal, I need to have the right cosets equal to right cosets, is the two left cosets are the cyclic and I?
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  4. #4
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    what is the two left and right coset there?
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