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Math Help - Normality

  1. #1
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    Normality

    Hi next one? Any ideas here?

    Let G be a group and  H \subset  G a subgroup such that |G/H| = 2. Show that H is normal in G.

    thnx
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  2. #2
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    We want to show that aH = Ha for any a in G to prove normality. If a in H then aH = H = Ha and proof is complete. If a not in H then aH is not H, similarly Ha is not H. But since there are only two cosets and both of them are not H it means they are the same so aH = Ha.
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