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Math Help - Is there a subgroup H of A4 such that A4 / H isomorphic to S3?

  1. #1
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    Is there a subgroup H of A4 such that A4 / H isomorphic to S3?

    Is there a subgroup H of A_4 such that the quotient group {A_4}/H \cong S_3? I know I could just go through the possibilities, but is there a very quick reason why the answer should be "no"?
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  2. #2
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    Quote Originally Posted by Boysilver View Post
    Is there a subgroup H of A_4 such that the quotient group {A_4}/H \cong S_3? I know I could just go through the possibilities, but is there a very quick reason why the answer should be "no"?

    As quick as possible: A_4 has no normal subgroups of order 2.

    Tonio
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  3. #3
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    Great, thanks.
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