# A particular subgroup of a Free Group is normal

1. Sep 22, 2011

### 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?

2. Sep 22, 2011

### micromass

Use this trick:

$$yx^ny^{-1}=(yxy^{-1})^n$$

3. Sep 22, 2011

### empyreandance

You saved me yet again! Thank you friend.