I am looking at the following:
Show that a torsion-free divisible group $G$ is a vector space over $\mathbb{Q}$.
I have no problem verifying the axioms of vector spaces after noting that the term divisible group $G$ implies that a solution to $ny=x$ exist where $n$ is an integer and is unique by the fact that the group $G$ is torsion-free.
What does vector spaces over $\mathbb{Q}$ mean? And why does the question say that it is a vector spaces over $\mathbb{Q}$ instead of $\mathbb{Z}$?