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Math Help - Abelian Group 2.12

  1. #1
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    Abelian Group 2.12

    Let {G;*} be a group such that a^2 = e for every a belonging to G. Prove that G must be a abelian group.
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  2. #2
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    Quote Originally Posted by tigergirl View Post
    Let {G;*} be a group such that a^2 = e for every a belonging to G. Prove that G must be a abelian group.
    <br />
a.b = b.a.a^{-1}.b^{-1}.a.b
    = b.a.a^{-1}.b^{-1}.(b.a).(b.a).a.b
    = b.a.e.e
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  3. #3
    Super Member Gamma's Avatar
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    a^2=e
    b^2=e
    abab=(ab)(ab)=(ab)^2=e
    Now take this and multiply on the left by a and right by b.

    a(abab)b=a(e)b
    (aa)ba(bb)=ab
    ba=ab
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