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Math Help - Show G it is a sdubgroup

  1. #1
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    Lightbulb Show G it is a sdubgroup

    For any x Є G, x-1Hx = {x-1hx: h Є H } is a subgroup of G.

    further show that O(H)= O(x-1Hx)
    Last edited by Aman3230; March 26th 2014 at 05:39 PM.
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  2. #2
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    Re: Show G it is a sdubgroup

    Interesting problem. What have you tried?
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  3. #3
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    Re: Show G it is a sdubgroup

    what do you mean by that...???
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  4. #4
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    Re: Show G it is a sdubgroup

    canet anybody solve it....?????
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  5. #5
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    Re: Show G it is a sdubgroup

    Suppose $a,b \in x^{-1}Hx$. Can you show that $ab^{-1} \in x^{-1}Hx$?

    (hint: first show that if $b = x^{-1}h'x$ that $b^{-1} = x^{-1}h'^{-1}x$ by multiplying the two together).

    Next show that the map:

    $h \mapsto x^{-1}hx$ is bijective between $H$ and $x^{-1}Hx$.

    (it is fairly obvious it's surjective, so concentrate on proving it's injective).
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