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Abelian group

  1. Sep 15, 2008 #1
    1. The problem statement, all variables and given/known data
    If G is a group such that (a*b)^2=(a^2)*(b^2) for all a,b in G, show that G must be abelian.


    3. The attempt at a solution
    First, I tried to expand the binomial (a*b)^2 and set it equal to (a^2)*(b^2). But then I didn't know where to go from there.
     
  2. jcsd
  3. Sep 15, 2008 #2

    Dick

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    You aren't trying very hard. A group is abelian if ab=ba for all a and b. (ab)^2=abab. (a^2)*(b^2)=aabb. Take it from there.
     
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