Let $G$ be a finite group which has a $G$-module $\mathbb{Q}/\mathbb{Z}$.
Note that $\frac{1}{n}\mathbb{Z}/\mathbb{Z}$ is $n$-torsion subgroup of $\mathbb{Q}/\mathbb{Z}$.
It is my purpose to give a map from $H^{i}(G;\mathbb{Q}/\mathbb{Z})$ to $H^{i}(G;\frac{1}{n}\mathbb{Z}/\mathbb{Z})$.
As we do for the singular cohomology with coefficients, my attempt is to use the tensor product $\otimes\frac{1}{n}\mathbb{Z}/\mathbb{Z}$.
However i am not sure that this is the right method for it.
Thank you for your time and effort.