I do not follow in the snippet below (taken from Advanced Modern Algebra, Rotman, Vol. 2,page 277,3rd edition) how it is meant that the target of $$\text{tor}_n^R(A,\ )$$ may be smaller or larger then $\mathbf{Ab}$ if $R=\mathbb{Q}$ or $R=\mathbb{Z}G$, respectively. I would say that it is not strictly larger in the case of $R=\mathbb{Z}G$ since it is exactly $\mathbf{Ab}$ here (i.e. $\mathbf{Ab}$ are just $\mathbb{Z}-$modules). I also cannot understand why it is smaller when $R=\mathbb{Q}$ ? I think that I'm confusing something here. Any detailed hint please ?
