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Math Help - Abelian

  1. #1
    Junior Member
    Joined
    Nov 2009
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    Abelian

    Hi can someone please help me with this question:

    Suppose that His a group in which x^2= e for all x in H.
    Prove that H
    is Abelian.


    Thanks
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  2. #2
    Member Haven's Avatar
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    Thanks
    8
    consider x,y \in G

    then consider (xy)^2 and x^ 2y^2
    <br />
(xy)^2 = xyxy = e
    x^2y^2 = xxyy = e
    \Rightarrow xyxy = xxyy
    Now use properties of Groups to show why the above equation implies that G is Abelian
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