  Let $ \sigma$ be a partition of the set of all primes and $\mathfrak{F}$ be a
hereditary formation. We proved that the $\mathfrak{F}$-hypercenter and the
intersection of weak $K$-$\mathfrak{F}$-subnormalizers of all Sylow subgroups
coincide if and only if $\mathfrak{F}$ is the class of all $\sigma$-nilpotent
groups. As corollary we obtained P. Hall's theorem about the intersection of
normalizers of Sylow subgroups.
