## Sylow Problem

Let $\displaystyle P$ be a $\displaystyle p-$ sylow subgroup of $\displaystyle G$ and suppose $\displaystyle a,b$ are in the center of $\displaystyle P$. Suppose furhter that $\displaystyle a=xbx^{-1}$ for some $\displaystyle x \in G$. Prove that there exists a $\displaystyle y \in N(P)$ such that $\displaystyle a=yby^{-1}$