Abstract Algebra- Conjugate Problem

corky23
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Homework Statement


Let G be a group of odd order, and a an element of G (not identity). Show that a and a^-1 are not conugate.


Homework Equations





The Attempt at a Solution


The only hint I have is to consider action of G on itself by conjugation.
 
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welcome to pf!

hi corky23! welcome to pf! :smile:
corky23 said:
The only hint I have is to consider action of G on itself by conjugation.

ok, then start by giving us your thoughts on that :wink:
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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