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Lower Bounds on the Number of Cyclic Subgroups in Finite Non-Cyclic Nilpotent Groups |
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| Authors: | Wei Meng & Jiakuan Lu |
| Abstract: | Let $G$ be a finite group and $\mathfrak{c}(G)$ denote the number of cyclic subgroups of $G$. It is known that the minimal value of $\mathfrak{c}$ 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 $\mathfrak{c}(G)$ are established. |
| Keywords: | $p$-groups cyclic subgroups Nilpotent groups |
| 点击此处可从《数学研究》浏览原始摘要信息 | |
