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A particular subgroup of a Free Group is normal

  1. Sep 22, 2011 #1
    Hello friends,

    I'm working through my book and I'm having a lot of trouble coming to terms / believing this. Could anyone assist?

    Let F be a free group and N be the subgroup generated by the set {x^n : x is in F and n is fixed} then N is normal in F.

    Any ideas?
     
  2. jcsd
  3. Sep 22, 2011 #2

    micromass

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    Use this trick:

    [tex]yx^ny^{-1}=(yxy^{-1})^n[/tex]
     
  4. Sep 22, 2011 #3
    You saved me yet again! Thank you friend.
     
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