I am reading Edwin Wiess' book called Cohomology of groups and I cant see why the following claim he makes is true in proposition 3-1-9.
He says that if $A$ is a finitely generated $G$-module for a finite group $G$ where $|G|=m$, that $A/mA$ is finite, where m is the multiplication by m map.
How does he know its finite? is this a standard result?
Thank you