Question
Determine all finite subgroups of $\mathbf{C}^{*}$, the group of nonzero complex numbers under multiplication.
Step 1
The group of nonzero complex numbers under multiplication can be expressed in polar form as \( z = re^{i\theta} \), where \( r > 0 \) is the modulus and \( \theta \) is the argument (angle) of the complex number. Show more…
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Let $G$ be an abelian group. Let $H$ be a subgroup of $G$, and let $K$ consist of all the elements $x$ in $G$ such that some power of $x$ is in $H$. That is, $K=\left\{x \in G:\right.$ for some integer $\left.n>0, x^{n} \in H\right\}$. Prove that $K$ is a subgroup of $G$.
SUBGROUPS
C
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