Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook