Mathematical Theory and Applications ›› 2026, Vol. 46 ›› Issue (02): 91-97.doi: 10.3969/j.issn.1006-8074.2026.02.006

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Finite Groups with Few Cyclic Subgroups

Kang Wangqiang1,  Wang Yu2,  Lu Jiakuan1,2,*, Meng Wei3   

  1. 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
  • Online:2026-06-28 Published:2026-07-15

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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

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