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Math Help - prove it is a subgroup

  1. #1
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    prove it is a subgroup

    Let G be a group and H be a subgroup of G. Define N(H)={x is a member of G|xHx^-1=H} Prove that N(H) (called normalizer of H) is a subgroup of G.
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  2. #2
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    Quote Originally Posted by mandy123 View Post
    Let G be a group and H be a subgroup of G. Define N(H)={x is a member of G|xHx^-1=H} Prove that N(H) (called normalizer of H) is a subgroup of G.
    This is a straightforward problem. Just use what it means is a definition of a subgroup. If x,y\in N(H) can you prove xy\in H? Once you prove closure the others ones should be even simpler.
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  3. #3
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    so would this work

    a^2=e and e^2=e so H is nonempty

    x,y is a member of N(H)
    x^2=e and y^2=e
    Prove (xy^-1)^2=e
    (ab^-1)^2= ab^-1 * ab^-1= a^2(b^-1)^2=a^2(b^2)^-1=ee^-1=e
    So xy^-1 belongs to N(H)
    So N(H) is a subgroup of G
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