Glauberman's theorem on intersection with the ZJ-subgroup

Statement

Suppose $G$ is a finite group, $p$ is an odd prime number, and $P$ is a $p$-Sylow subgroup. Suppose, further, that $B$ is a nontrivial normal $p$-subgroup of $G$. Then, $B\cap Z(J(P))$ is also a nontrivial normal $p$-subgroup of $G$.