### Li Zhang

University of Scinece and Technology of China, Hefei, China### Xiaoyu Chen

Nanjing Normal University, China### Wenbin Guo

University of Scinece and Technology of China, Hefei, China

## Abstract

Let $\mathfrak{F}$ be a class of groups and $G$ a finite group. A chief factor $H/K$ of $G$ is called *$\mathfrak{F}$-central in* $G$ provided $(H/K)\rtimes (G/C_{G}(H/K))\in\mathfrak{F}$. A normal subgroup $N$ of $G$ is said to be *$\pi\mathfrak{F}$-hypercentral in* $G$ if every chief factor of $G$ below $N$ of order divisible by at least one prime in $\pi$ is $\mathfrak{F}$-central in $G$. The $\pi\mathfrak{F}$-hypercentre of $G$ is the product of all the normal $\pi\mathfrak{F}$-hypercentral subgroups of $G$. In this paper, we study the structure of finite groups by using the notion of $\pi\mathfrak{F}$-hypercentre. New characterizations of some classes of finite groups are obtained.

## Cite this article

Li Zhang, Xiaoyu Chen, Wenbin Guo, On $\pi\mathfrak{F}$-supplemented subgroups of a finite group. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 175–189

DOI 10.4171/RSMUP/136-12