Finite Groups All of Whose Subgroups are P-Subnormal or TI-Subgroups

被引：0

作者：

Ballester-Bolinches, A. ^{[1
,2
]}

Kamornikov, S. F. ^{[3
]}

Perez-Calabuig, V. ^{[2
]}

Yi, X. ^{[4
]}

机构：

[1] Guangdong Univ Educ, Dept Math, Guangzhou 510303, Peoples R China

[2] Univ Valencia, Dept Matemat, Dr Moliner,50, Burjassot 46100, Valencia, Spain

[3] Francisk Skorina State Gomel Univ, Gomel 246019, BELARUS

[4] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2024年 / 21卷 / 02期

关键词：

Finite group; P-subnormal subgroup; TI-subgroup; TRIVIAL INTERSECTION;

D O I：

10.1007/s00009-024-02612-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let P be the set of all prime numbers. A subgroup H of a finite group G is said to be P-subnormal in G if there exists a chain of subgroups H=H-0 subset of H-1 subset of<middle dot><middle dot><middle dot>subset of Hn-1 subset of H-n=G such that eitherH(i-1)is normal inH(i)or|H-i:Hi-1|is a prime number for every i=1,2,...,n. A subgroup H of G is called a TI-subgroup if every pair of distinct conjugates of H has trivial intersection. The aim of this paper is to give a complete description of all finite groups in which every non-P-subnormal subgroup is a TI-subgroup

引用

页数：9

共 10 条

[1]

Ballester-Bolinches A., 2006, CLASSES FINITE GROUP

[2] ON TRIVIAL INTERSECTION OF CYCLIC SYLOW SUBGROUPS [J].