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Commutator question.

  1. Mar 7, 2009 #1

    MathematicalPhysicist

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    Perhaps someone will help me in this.
    I need to prove that the group [G,G] of elements of the form [tex]gh g^{-1}h^{-1}[/tex] where g,h in G, is normal in G, i.e if k is in G, then [tex]kghg^{-1}h^{-1}k^{-1}=aba^{-1}b^{-1}[/tex] for some a,b in G.
    I tried writing it as [tex]kghkk^{-1}g^{-1}h^{-1}k^{-1}[/tex], but here is where my attmempt run down the mill, as in not successful.
    Any hints?
     
  2. jcsd
  3. Mar 7, 2009 #2
    Conjugate two elements g,h by the same element and compute the commutator.
     
  4. Mar 7, 2009 #3

    MathematicalPhysicist

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    Ok, thanks.
     
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