  In this paper some properties of the $\mathfrak{F}^*$-hypercenter of a finite
group are studied where $\mathfrak{F}^*$ is the class of all finite
quasi-$\mathfrak{F}$-groups for a hereditary saturated formation $\mathfrak{F}$
of finite groups. In particular, it is shown that the quasinilpotent
hypercenter of a finite group coincides with the intersection of all maximal
quasinilpotent subgroups.
