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Math Help - order of the center

  1. #1
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    order of the center

    Let G be a finite group and H be a normal subgroup of order 2. Then order if the center of G is
    a) 0
    b) 1
    c) An even integer >=2
    d) An odd integer >=3

    I know a0 is not right. I think we have to use class eqn. but I dont know ho to proceed.
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  2. #2
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    Quote Originally Posted by poorna View Post
    Let G be a finite group and H be a normal subgroup of order 2. Then order if the center of G is
    a) 0
    b) 1
    c) An even integer >=2
    d) An odd integer >=3

    I know a0 is not right. I think we have to use class eqn. but I dont know ho to proceed.


    Prove: if a group has a normal subgroup of order 2 then this subgroup is central (i.e., it is contained in the group's center). ( hint: very easy proof: uses the fact that conjugate elements have the same order... )

    Tonio
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