On the quasi-$\mathfrak{F}$-hypercenter of a finite group

TL;DR

This paper investigates the properties of the $rak{F}^*$-hypercenter in finite groups, revealing its relation to maximal quasinilpotent subgroups within the context of hereditary saturated formations.

Contribution

It introduces and analyzes the $rak{F}^*$-hypercenter for finite groups, connecting it to quasinilpotent hypercenters and maximal subgroups, expanding understanding of group structure.

Findings

The $rak{F}^*$-hypercenter coincides with the intersection of all maximal quasinilpotent subgroups.

Properties of the $rak{F}^*$-hypercenter are characterized within hereditary saturated formations.

The paper establishes new links between hypercenters and subgroup intersections in finite groups.

Abstract

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.