On a problem posed by S. Li and J. Liu

被引：6

作者：

Ballester-Bolinches, Adolfo ^{[1
]}

Qiao, ShouHong ^{[2
]}

机构：

[1] Univ Valencia, Dept Algebra, E-46100 Valencia, Spain

[2] Guangdong Univ Technol, Sch Appl Math, Guangzhou 510006, Guangdong, Peoples R China

来源：

ARCHIV DER MATHEMATIK | 2014年 / 102卷 / 02期

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Finite group; Soluble group; Hall subgroups;

D O I：

10.1007/s00013-014-0617-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A subgroup H of a finite group G is said to be Hall normally embedded in G if there is a normal subgroup N of G such that H is a Hall subgroup of N. The aim of this note is to prove that a group G has a Hall normally embedded subgroup of order |B| for each subgroup B of G if and only if G is soluble with nilpotent residual cyclic of square-free order. This is the answer to a problem posed by Li and Liu (J. Algebra 388:1-9, 2013).

引用

页码：109 / 111

页数：3