My question is referring to the answer in this link
especially to this sentence:
"if $G$ is a finite group and $M$ is a $Z_p[G]$-module, then $M$ is (in)decomposable if and only if $M/p^kM$ is a (in)decomposable $Z/p^kZ[G]$-module for some $k$."
Why is it easier to determine the number of the indecomposable $Z/p^kZ[G]$-modules for some $k$ which have the form $M/p^kM$. Do I really have to search first for the indecomposable $M/p^kM$-modules for each $k=1,\cdots,d$, with $d$ minimal in $1=p^d$. And then look if one can write this modules in the form $M/p^kM$? This seams quite difficult for me.
Thank you for hints how to solve this.