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Is it true that if $G$ is a divisible group then any subgroup of G is also divisible?

I know that if $H \leq G$ then for any $h \in H$ and for any $k \in \mathbb{N}$ then there exists $x \in G$ such that $x^{k}=h$, therefore I can show that $x^{k} \in H$. But, is it always true that $x \in H$ or there exists a counterexample?

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The group $\mathbb{Q}$ of rational numbers under addition is divisible. The group $\mathbb{Z}$ of integers is a subgroup, but is not divisible.

It is, however, true that every quotient of a divisible group is divisible.

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