On finite groups with semisubnormal residuals of Sylow normalizers

Let $\pi$ be some set of primes, $G$ be a $\pi$-soluble group and $G\in\mathfrak{E}_\pi\mathfrak{E}_{\pi'}$. It is proved that if for any prime $p\in\pi\cap\pi(G)$ and Sylow $p$-subgroup $P$ from $G$ the normalizer $N_G(P)$ is $\pi$-supersoluble and its nilpotent residual is semisubnormal in $G$, then $G$ is $\pi$-supersoluble.