Lower Bounds on the Number of Cyclic Subgroups in Finite Non-Cyclic Nilpotent Groups

被引：0

作者：

Meng, Wei ^{[1
]}

Lu, Jiakuan ^{[2
]}

机构：

[1] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541004, Peoples R China

[2] Guangxi Normal Univ, Sch Math & Stat, Guilin 541004, Peoples R China

来源：

JOURNAL OF MATHEMATICAL STUDY | 2023年 / 56卷 / 01期

关键词：

p-groups; cyclic subgroups; Nilpotent groups;

D O I：

10.4208/jms.v56n1.23.03

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group and c(G) denote the number of cyclic subgroups of G. It is known that the minimal value of c on the set of groups of order n, where n is a positive integer, will occur at the cyclic group Z(n). In this paper, for non-cyclic nilpotent groups G of order n, the lower bounds of c(G) are established.

引用

页码：93 / 102

页数：10

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