On Sylow permutable subgroups of finite groups

被引：1

作者：

Ballester-Bolinches, Adolfo ^{[1
]}

Heineken, Hermann ^{[2
]}

Spagnuolo, Francesca ^{[1
]}

机构：

[1] Univ Valencia, Dept Matemat, Dr Moliner 50, E-46100 Valencia, Spain

[2] Univ Wurzburg, Math Inst, D-97074 Wurzburg, Germany

来源：

FORUM MATHEMATICUM | 2017年 / 29卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Finite groups; subnormal subgroups; permutability; S-permutability;

D O I：

10.1515/forum-2016-0262

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A subgroup H of a group G is called Sylow permutable, or S-permutable, in G if H permutes with all Sylow p-subgroups of G for all primes p. A group G is said to be a PST-group if Sylow permutability is a transitive relation in G. We show that a group G which is factorised by a normal subgroup and a subnormal PST-subgroup of odd order is supersoluble. As a consequence, the normal closure S-G of a subnormal PST-subgroup S of odd order of a group G is supersoluble, and the subgroup generated by subnormal PST-subgroups of G of odd order is supersoluble as well.

引用

页码：1307 / 1310

页数：4

共 8 条

[1] Some special classes of finite soluble PST-groups [J].