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Group question

  1. Dec 15, 2005 #1
    in a non abelian group does (ab)^2 = (b^2)(a^2)?
    this isnt homework, my semester is over.
     
  2. jcsd
  3. Dec 15, 2005 #2

    matt grime

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    1. Just expand (ab)^2

    2. Or look in the smallest non abelian group there is: S_3
     
  4. Dec 15, 2005 #3
    it expands to abab , but how come (ab)^-1 = (b^-1)(a^-1)?
     
  5. Dec 15, 2005 #4

    matt grime

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    because inversion reverses the order of the elements, it is an anti-automorphism and has nothing to do with the commutativity or otherwise of the group.

    we know the inverse of ab is a c such that abc=1, bc=a^{-1}, and then c=b^{-1}a^{-1}
     
  6. Dec 15, 2005 #5
    ok, thanks.
     
  7. Dec 16, 2005 #6

    HallsofIvy

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    What do you get if you multiply (ab)(b-1a-1)?
     
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