# Finite groups with $H_{L}$-embedded subgroups

### Bin Hu

Jiangsu Normal University, Xuzhou, China### Jianhong Huang

Jiangsu Normal University, Xuzhou, China### Alexander N. Skiba

Francisk Skorina Gomel State University, Belarus

## Abstract

Let $G$ be a finite soluble group and let $F$ be a class of groups. A chief factor $H/K$ of $G$ is said to be $F$-central (in $G$) if $(H/K)⋊(G/C_{G}(H/K))∈F$; we write $L_{cF}(G)$ to denote the set of all subgroups $A$ of $G$ such that every chief factor $H/K$ of $G$ between $A_{G}$ and $A_{G}$ is $F$-central in $G$. Let $L$ be a set of subgroups of $G$. We say that a subgroup $A$ of $G$ is $H_{L}$-embedded in $G$ provided $A$ is a Hall subgroup of some subgroup $E∈L$. In this paper, we study the structure of $G$ under the condition that every subgroup of $G$ is $H_{L}$-embedded in $G$, where $L=L_{cF}(G)$ for some hereditary saturated formation $F$. Some known results are generalized.

## Cite this article

Bin Hu, Jianhong Huang, Alexander N. Skiba, Finite groups with $H_{L}$-embedded subgroups. Rend. Sem. Mat. Univ. Padova 148 (2022), pp. 51–63

DOI 10.4171/RSMUP/102