Automorphisms of a group G

Dummit and Foote Section 4.4 Automorphisms Exercise 1 reads as follows:

Let and is conjugation by g, prove that = .

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A start to the proof is as follows:

=

=

=

Now we have completed the proof if

But why is in this case??

Can anyone please help clarify this situation?

Peter

Re: Automorphisms of a group G

I have now thought about this and suspect that the answer to my own question is as follows:

For an automorphism we have

Thus

and from this it follows that

Am I correct?

Peter

Re: Automorphisms of a group G

Quote:

Originally Posted by

**Bernhard** I have now thought about this and suspect that the answer to my own question is as follows:

For an automorphism we have

Thus

and from this it follows that

Am I correct?

Peter

Yes, that is correct.