On the quasi-$\mathfrak{F}$-hypercenter of a finite group
  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. 
V.I. Murashka
math.GR