- #1

WWGD

Science Advisor

Gold Member

2019 Award

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## Main Question or Discussion Point

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?

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?