I have been looking a cohomology where it is known that uniquely divisible modules have trivial cohomology. But in the case of $\mathbb{Z}$-modules I know $\mathbb{Q}$ has trivial cohomology since its "uniquely divisible" but $\mathbb{Q}/\mathbb{Z}$ is not cohomologically trivial but they are both divisible groups, so what exactly is the definition of a divisible group? Since I want to see if $Hom(L,\mathbb{R})$ is uniquely divisible (L some abelian group) but im not quite sure how to do this since I dont know a good definition of uniquely divisible
Thank you