# A particular subgroup of a Free Group is normal

by empyreandance
Tags: free, normal, subgroup
 P: 15 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?
 PF Patron Sci Advisor Thanks Emeritus P: 15,673 Use this trick: $$yx^ny^{-1}=(yxy^{-1})^n$$
 P: 15 You saved me yet again! Thank you friend.

 Related Discussions Calculus & Beyond Homework 3 Calculus & Beyond Homework 7 Calculus & Beyond Homework 4 Linear & Abstract Algebra 0 Differential Geometry 1