For a finite group G and a finite field $\mathbb{F}_p$ of characteristic $p$,
  J($\mathbb{F}_{p^k} \otimes_{\mathbb{F}_p }\mathbb{F}_p G ) = J(\mathbb{F}_{p^k}G)$? where $J(\mathbb{F}_{p^k}G)$ is the Jacobson radical of the group algebra $\mathbb{F}_{p^k}G$ and $\mathbb{F}_{p^k}$ is an extension field of $\mathbb{F}_p$.