Prove that if in a group G, then . My proof so far: Now (ab)^{2}=a^{2}b^{2} for each a,b \in G, so implies then, there exist a^{-1},b^{-1} in G (a^-1)(a^2b^2)(b^-1) = (a^-1)(b^2a^2)(b^-1) ab=ba. Am I allow to switch the a and b like that?
Last edited by tttcomrader; Aug 25th 2007 at 03:27 PM.
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Originally Posted by tttcomrader Prove that if in a group G, then . Have you written the problem correctly? Or should it be ??? If you do mean that then:
Last edited by Plato; Aug 25th 2007 at 03:26 PM.
Oops, yeah, that is right.
Please see my edit.
Thank you, sir, that is really easy, I really should have gotten it myself.
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