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Math Help - Algebra Help. Groups..

  1. #1
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    Red face Algebra Help. Groups..

    Let <G, *> be a group, x, a, b ∈ G and e is the identify element. Prove that if a2 = e and a*x*a = x3, then x8 = e.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Algebra Help. Groups..

    Quote Originally Posted by mous99 View Post
    Let <G, *> be a group, x, a, b ∈ G and e is the identify element. Prove that if a2 = e and a*x*a = x3, then x8 = e.
    Prove that x=ax^3a. Then, x^8=x^9x^{-1}=(axa)^3x^{-1}=\ldots=e.
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    Re: Algebra Help. Groups..

    how to prove a*x*a = x3 ?
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: Algebra Help. Groups..

    Quote Originally Posted by mous99 View Post
    how to prove a*x*a = x3 ?
    You can't prove a hypothesis.
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  5. #5
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    Re: Algebra Help. Groups..

    can u show be by step? thankssssss
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  6. #6
    MHF Contributor FernandoRevilla's Avatar
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    Re: Algebra Help. Groups..

    Quote Originally Posted by mous99 View Post
    can u show be by step? thankssssss
    Better, ask me step by step.
    Thanks from Bingk
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