Finite non-cyclic nilpotent group whose number of subgroups is minimal

被引：2
作者：
Meng, Wei [1 ]
Lu, Jiakuan [2 ]
机构：
[1] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541004, Guangxi, Peoples R China
[2] Guangxi Normal Univ, Sch Math & Stat, Guilin 541004, Guangxi, Peoples R China
来源：
RICERCHE DI MATEMATICA | 2024年 / 73卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Subgroup counting; Nilpotent groups; Sylow subgroups; CYCLIC SUBGROUPS;
D O I：
10.1007/s11587-021-00584-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a finite group and s(G) denote the number of subgroups of G. Aivazidis and Muller proved that if G is a non-cyclic p-group of order p(lambda), then s(G) >= 6 whenever p(lambda) = 2(3); s(G) >= (p + 1)(lambda - 1) + 2 whenever p(lambda) not equal 2(3). In this paper, we generalize the results of Aivazidis and Muller on all finite non-cyclic nilpotent groups. Lower bounds on s(G) of non-cyclic nilpotent groups G are established.
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页码：191 / 198
页数：8
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