A particular subgroup of a Free Group is normal

empyreandance

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?

micromass

Use this trick:

[tex]yx^ny^{-1}=(yxy^{-1})^n[/tex]

empyreandance

You saved me yet again! Thank you friend.

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empyreandance	A particular subgroup of a Free Group is normal Tweet 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?

micromass Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus	Use this trick: [tex]yx^ny^{-1}=(yxy^{-1})^n[/tex]