This question is maybe too simple, but I am just wondering. In the study of modules, divisible group is introduced, but specifically only for abelian groups (in Hungerford, for example). Something like: "An abelian group $G$ is called divisible if for each $a\in G$ and nonzero integer $n$, there is $b\in G$ such that $a=nb$"
It seems like it can also be defined for non abelian groups. I have searched in other sources but could not understand the main reason. I know modules are abelian groups, but is that the only reason why divisibility is introduced only for abelian groups in such textbook? I mean, usually if it can, author will just define it for general group by simply removing the word "abelian", and then use it for abelian groups without problem, right? Maybe there is another reasoning I miss.
Thanks in advance.