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Abstract Abgebra proof

  1. Jul 20, 2010 #1
    Let G be a group. Show (xy)[tex]^{-1}[/tex] = x[tex]^{-1}[/tex]y[tex]^{-1}[/tex] for all x, g [tex]\in[/tex] G if and only if G is abelian.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 20, 2010 #2
    I think you're done :)
     
  4. Jul 20, 2010 #3

    Mark44

    Staff: Mentor

    What have you tried?
     
  5. Jul 20, 2010 #4

    hunt_mat

    User Avatar
    Homework Helper

    The element [tex](xy)^{-1}[/tex] is the inverse element of [tex]xy[/tex] and therefore [tex](xy)^{-1}xy=e[/tex] where e is the identity, so...
     
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