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A particular subgroup of a Free Group is normal

by empyreandance
Tags: free, normal, subgroup
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empyreandance
#1
Sep22-11, 03:58 PM
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?
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micromass
#2
Sep22-11, 04:46 PM
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P: 18,036
Use this trick:

[tex]yx^ny^{-1}=(yxy^{-1})^n[/tex]
empyreandance
#3
Sep22-11, 10:34 PM
P: 15
You saved me yet again! Thank you friend.


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