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Math Help - Non-abelian group question

  1. #1
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    Non-abelian group question

    To show that a non-abelian group has elements a,b and c such that xy = yz and x≠z,

    Would this be the correct approach?


    For some x, y in a non-abelian group G


    xy≠yx


    and if


    xy = yz for some z in G


    then x≠z otherwise


    xy≠yx


    Is not satisfied for elements x and y of the group.

    Is more detail required?

    I feel like it is too straight forward

    Thanks in advance
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  2. #2
    Member Sylvia104's Avatar
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    Re: Non-abelian group question

    Your proof is almost complete. You state that

    Quote Originally Posted by Daniiel View Post
    and if


    xy = yz for some z in G


    then x≠z otherwise


    xy=yx
    To complete the proof, you need to state that such an element z exists, namely z=y^{-1}xy.
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  3. #3
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    Re: Non-abelian group question

    Thanks very much Sylvia!
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