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Homework Help: Prove commutative

  1. Aug 31, 2010 #1
    (A) Let (G,*) be a group such that x*x=eG for all x in G. Prove G is commutative.
    (B) Give a specific example of an infinite group (G,*) such that x*x=eG for all x in G.

    I have not gotten very far, just to let two variable x,y be in G and I know that (x*y)*(x*y) = eG .. I'm not sure where to go from here..
  2. jcsd
  3. Aug 31, 2010 #2
    Well, for a, you know ...
    (xy)^{-1} = y^{-1}x^{-1}

    Try multiplying that to both sides of the equality you presented, and see what you get.
  4. Aug 31, 2010 #3
    hmm can i ask, what's "eG" means?? identity?
  5. Aug 31, 2010 #4
    so, will i just get eG on both sides? does this prove that it is commutative? I'm confused.
  6. Aug 31, 2010 #5
    yes, it is the identity
  7. Aug 31, 2010 #6
    You won't get eG on both sides. I'm saying, multiply what I showed you to both sides of

    xyxy = e_{G}
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