Properties, General Results on of Aut(G) ?

Gold Member
Hi, just curious: I saw a result that for the multiplicative group G:= {1,-1, i, -i } , "every

homomorphism ## h: G \rightarrow G ## is of the form ## z \rightarrow z^k ## for some

##k \in \mathbb Z ##. I can show this is true by considering the image of a generator, but

I was wondering if there are general results about the automorphism groups that may also

apply. Any ideas?

Gold Member
I think this has to see with the fact that this G is cyclic. Then once we know the value of ## z^k## for some generator, we know the
whole homomorphism. But that is not a proof.

lavinia