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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 ...
    [tex]
    (xy)^{-1} = y^{-1}x^{-1}
    [/tex]

    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

    [tex]
    xyxy = e_{G}
    [/tex]
     
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