A NOTE ON FINITE GROUPS WITH FEW TI-SUBGROUPS

被引：2

作者：

Shi, Jiangtao ^{[1
]}

Huang, Jingjing ^{[2
]}

Zhang, Cui ^{[1
]}

机构：

[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China

[2] Commun Univ China, Fac Sci & Technol, Beijing 100024, Peoples R China

来源：

INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA | 2018年 / 23卷

关键词：

Non-metacyclic subgroup; TI-subgroup; normal; solvable; Sylow tower;

D O I：

10.24330/ieja.373640

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In [Comm. Algebra, 43(2015), 2680-2689], finite groups all of whose metacyclic subgroups are TI-subgroups have been classified by S. Li, Z. Shen and N. Du. In this note we investigate a finite group all of whose non-metacyclic subgroups are TI-subgroups. We prove that G is a group all of whose non-metacyclic subgroups are TI-subgroups if and only if all non-metacyclic subgroups of G are normal. Furthermore, we show that a group all of whose non-cyclic subgroups are TI-subgroups has a Sylow tower.

引用

页码：42 / 46

页数：5

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