循环子群个数较少的有限群

康旺强¹, 王宇², 卢家宽^1,2,*,孟伟³

1. 桂林学院信息工程学院, 桂林 541006; 2. 广西师范大学数学与统计学院, 桂林 541001; 3. 桂林电子科技大学数学与计算科学学院, 桂林 54100

Kang Wangqiang^1, Wang Yu², Lu Jiakuan^1,2,*, Meng Wei³

1. School of Information Engineering, Guilin University, Guilin 541006, China; 2. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541001, China; 3. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China

摘要： 设~$G$~ 是有限群,~$c(G)$~表示群~$G$~的循环子群的个数.~本文讨论~$c(G)$~较小时有限群~$G$~的结构, 并给出相应的同构分类.

关键词: 有限群, 循环子群, 可解群

Abstract:

Let $G$ be a finite group and $c(G)$ denote the number of cyclic subgroups of $G$. In this paper, we discuss the

structure of finite groups $G$ when $c(G)$ is small, and provide their isomorphic classifications.

Key words: Finite group, Cyclic subgroup, Solvable group

康旺强, 王宇, 卢家宽, 孟伟. 循环子群个数较少的有限群[J]. 数学理论与应用, 2026, 46(02): 91-97.

Kang Wangqiang, Wang Yu, Lu Jiakuan, Meng Wei. Finite Groups with Few Cyclic Subgroups[J]. Mathematical Theory and Applications, 2026, 46(02): 91-97.

PDF