A particular subgroup of a Free Group is normal

empyreandance
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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?
 
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Use this trick:

yx^ny^{-1}=(yxy^{-1})^n
 
You saved me yet again! Thank you friend.
 

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