Abstract Algebra- Conjugate Problem

[corky23]

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.

 

[tiny-tim]

welcome to pf!

hi corky23! welcome to pf!

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