Hello? I have a simple question.

Is $\mathbb{Z}_p$ flat $\mathbb{Z}_pG$-module for a finite $p$-group $G$? Here, $p$ is prime and $\mathbb{Z}_p$ means the integers localized at $(p)$. If not, is it false even for a finite abelian $p$-group $G$?

Please let me know.