I'm reading "Contemporary Abstract Algebra," by Gallian.

This is based on exercises 3.45 and 4.15 ibid.

What is $H_G^{(n)}:=\{h\in G: \operatorname{ord}(h)\mid n\}$ called for any fixed abelian group $G$ and $n\in\Bbb N$?

Here $\operatorname{ord}(g)$ is the order of $g$ in $G$.

I suspect that $H_G^{(n)}\le G$, always.

NB: The $H_G^{(n)}$ is my own notation.


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