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Groups whose elements have order 2

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    suppose that G is a group in which every non-identity element has order two. show that G is commutative.



    2. Relevant equations



    3. The attempt at a solution
    IS THIS CORRECT??????

    ab=a[(ab)^2]b=(a^2)(ba)(b^2)=ba
     
  2. jcsd
  3. Oct 20, 2009 #2

    lanedance

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    yeah looks good (same as last post), if you want to include every step
    ab = (ae)b = aeb = a (abab) b = (aa) ba (bb) = ebae = ba
    does assume the multiplication is associative
     
  4. Oct 20, 2009 #3

    Dick

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    Will you please stop posting the same question over and over again?
     
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