• anonymous
Let $$G=\left{z\in\mathbb{C}|z^n=1\text{ for some }n\in\mathbb{Z}^+\right}$$. Prove that for any fixed integer $$k > 1$$ the map from G to itself defined by $$z \mapsto z^k$$ is a surjective homomorphism but not an isomorphism. I can show that it's a homomorphism, but am a bit stuck after that
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