I just started with group theory. I know that for any finite group $G$, the number of elements of order $n$ in group $G$ will be multiple of $\phi(n)$ where $\phi$ is the Euler phi function. But what can I conclude about the number of elements of order $n$ when $G$ is infinite? Is there a relation with the theorem of finite groups?
2026-03-28 00:30:58.1774657858
If $G$ is an infinite group, what can you say about the number of elements of order $n$ in the group?
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Nothing, without knowing more about the group. $(\mathbb Z, +)$ has no such elements, for example.