Thread: Conjugation a Isomorphism?

Hey,

I'm having a bit of trouble w/ this one....

Let G be a group and let a be in G. Define a map Phi: G -> G by Phi(g) = a^-1 g a. Is phi an isomorphism? If so, prove it.

Thanks in advance

Originally Posted by bakerconspiracy

Hey,

I'm having a bit of trouble w/ this one....

Let G be a group and let a be in G. Define a map Phi: G -> G by Phi(g) = a^-1 g a. Is phi an isomorphism? If so, prove it.

Thanks in advance

What's the problem? Indeed, conjugation is an automorphism.

Tonio

Now, what more do you need to show that it is an isomorphism?