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

作　　者：Wei Meng Jiakuan Lu 

机构地区：[1]School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China [2]School of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China

出　　处：《Journal of Mathematical Study》2023年第1期93-102,共10页数学研究（英文）

基　　金：supported by Guangxi Natural Science Foundation Program(Grant No.2021JJA10003);National Natural Science Foundation of China(Grant No.12161021);Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation;J.K.Lu is supported by National Natural Science Foundation of China(Grant No.11861015);Guangxi Natural Science Foundation Program(Grant No.2020GXNSFAA238045).

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 Zn.In this paper,for non-cyclic nilpotent groups G of order n,the lower bounds of c(G)are established.

关 键 词：P-GROUPS cyclic subgroups Nilpotent groups 

分 类 号：O152[理学—数学]