1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook