$G$ is a finite solvable group. Let$\{P_{1}, P_{2}, \ldots , P_{s}\}$ be a Sylow basis of $G$. We have that $G=P_{1}P_{2}\cdots P_{s}$. Set \begin{equation} \begin{aligned} T=\prod\limits_{t=1}^{s-1}P_t, H=\prod\limits_{k\neq3}^sP_k, K=\prod\limits_{r\neq2}^sP_r.\nonumber \end{aligned} \end{equation} Suppose that $T$ is nilpotent(i.e. $T=P_{1}\times P_{2}\times P_{3}\times \cdots \times P_{s-1}$), $N_H(P_s)=P_s$ and $N_K(P_s)=P_s$.

Can we get that $N_G(P_s)=P_s$