Hi,

Can someone help me with proving this proposition:

Let a group. For we define:

Proof is an automorphism of (We call it an inside automorphism of determined by ).

If I wan't to proof is an automorphism I've to demonstrate that is an isomorphism or an bijective homomorphism.

1) is an homorphism

But to prove if is an homorphism in my inion I need a composite law for the group .

I guess I've to proof for two arbitrary chosen numbers in that:

But how do I now: ? Or doesn't that matter? ...

2) is bijective:

I've to prove that:

In this case:

This is true because in a group a is the symmetric element of and so:

So the only thing I haven't proved yet is the homorphism. Does someone have a hint?

Thanks in advance! .

(Sorry If my English wouldn't be correct, but English mathematical terminology is not easy for me as a Belgian).