I would like to know how exactly the module structure on $\mathbb{Z}$ as a module over the group ring $\mathbb{Z}[G]$ works.
Obviously, we take just the usual addition on $\mathbb{Z}$, but how does taking a product between an element of $\mathbb{Z}[G]$ and an integer work?
Some of you mentioned one needs a groupaction of G on $\mathbb{Z}$. Given such an action, my question remains the same. And since apparently in the context of group (co)homology this action is trivial (which is precicsely the context here), how would this look in this trivial case?
Thanks