Finite Nilpotent Groups Whose Cyclic Subgroups are TI-Subgroups

被引：4

作者：

Abdollahi, Alireza ^{[1
,2
]}

Mousavi, Hamid ^{[3
]}

机构：

[1] Univ Isfahan, Dept Math, Esfahan 8174673441, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

[3] Univ Tabriz, Dept Math, POB 51666-17766, Tabriz, Iran

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2017年 / 40卷 / 04期

关键词：

TI-group; CTI-groups; p-Group; ABELIAN SUBGROUPS; TRIVIAL INTERSECTION; P-GROUPS;

D O I：

10.1007/s40840-015-0151-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A subgroup H of a group G is called a TI-subgroup if H-g boolean AND H = 1 or H for all g is an element of G; and H is called quasi TI if C-G(x) <= N-G(H) for all non-trivial elements x is an element of H. A group G is called (quasi CTI-group) CTI-group if every cyclic subgroup of G is a (quasi TI-subgroup) TI-subgroup. It is clear that TI subgroups are quasi TI. We first show that finite nilpotent quasi CTI-groups are CTI. In this paper, we classify all finite nilpotent CTI-groups.

引用

页码：1577 / 1589

页数：13

共 11 条

[1]

[Anonymous], 1967, ENDLICHE GRUPPEN

[2] On subgroups of finite p-groups [J].