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Math Help - Normalizer as a subgroup. Unique largest subgroup in which A is normal.

  1. #1
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    Post Normalizer as a subgroup. Unique largest subgroup in which A is normal.

    Prove that the normalizer of A \subseteq G is always a subgroup of G which contains A. Further prove it is the unique largest subgroup in which A is normal.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by joestevens View Post
    Prove that the normalizer of A \subseteq G is always a subgroup of G which contains A. Further prove it is the unique largest subgroup in which A is normal.
    What particularly are you having trouble with?
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  3. #3
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    Quote Originally Posted by Drexel28 View Post
    What particularly are you having trouble with?
    Am I supposed to show A \subseteq N(A) \subseteq G or just that N(A) \subseteq G, when A \subseteq G?
    Where should I start?
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