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

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.