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Nonabelian finite group G

  1. Aug 17, 2010 #1
    Hi,

    This is not a homework question. I am a trying to prove a result for myself, and the question is can I always find, in a nonabelian finite group G, and some fixed proper subgroup S < G, two distinct elements, which we shall call x and y, outside of S, such that the cosets Sx = Sx^{-1}, and Sy = Sy^-1. That is, can we always find elements x, y outside of S such that x and its inverse x^{-1} both belong to some coset of S, while y and y^{-1} belong to a different, disjoint coset of S.

    Sincerely, Nici.
     
  2. jcsd
  3. Aug 17, 2010 #2

    Office_Shredder

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    Re: Cosets

    If Sx=Sx-1 multiply both cosets by x to get Sx2=S. What does this tell us about x2?
     
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