We have $(\Bbb C^*, .)$ so i want to prove that all finite subgroups of $\Bbb C^*$ are cyclic. But i don't know how start the proof.
Then if it is cyclic, have to prove that if $H$ is a subgroup of $\Bbb C^*$ then $H = G_n$ with $n \in \Bbb N$. but this part is more simple because let $h$ in $H$ that $h^n=1$ then $h=e^{\frac{2\pi i k}{n}}$ with $k \in \{1,2, \dots, n-1 \}$ that is a generator of $G_n$
i'm in right?
