If G is a finite group and its p-Sylow subgroup P lies in the center of G, prove that there exists a normal subgroup N of G with $P \cap N =e$ and PN=G
Burnside's theorem: if $P$ is a Sylow subgroup of a group $G$ and $P \subseteq Z(N_G(P)),$ then there exists a normal subgroup $N$ of $G$ such that $P \cap N=\{1\}$ and $G=PN.$