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Math Help - G is a finite group

  1. #1
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    G is a finite group

    G is a finite group and x\in G and |x|=m. Prove that if m is odd, then x=(x^2)^k for some k\in\mathbb{Z}, k\geq 1

    x^m=x^{2k+1}=(x^{2})^kx

    I need k to be 0 though. What am I missing?
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  2. #2
    A Plied Mathematician
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    Re: G is a finite group

    Try letting m=2k-1, instead of m=2k+1. Also, you have to use the order of x to get another equation that will prove useful.
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  3. #3
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    Re: G is a finite group

    Quote Originally Posted by Ackbeet View Post
    Also, you have to use the order of x to get another equation that will prove useful.
    ???????
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  4. #4
    A Plied Mathematician
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    Re: G is a finite group

    What does |x| = m mean? Can you wrote down an equation that says the same thing?
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  5. #5
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    Re: G is a finite group

    Quote Originally Posted by Ackbeet View Post
    What does |x| = m mean? Can you wrote down an equation that says the same thing?
    Ok ok.
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