Volume 56, Issue 1
Lower Bounds on the Number of Cyclic Subgroups in Finite Non-Cyclic Nilpotent Groups

Wei Meng & Jiakuan Lu

J. Math. Study, 56 (2023), pp. 93-102.

Published online: 2022-11

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  • 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.

  • AMS Subject Headings

20D10, 20D20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mlwhappyhappy@163.com (Wei Meng)

jklu@gxnu.edu.cn (Jiakuan Lu)

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@Article{JMS-56-93, author = {Meng , Wei and Lu , Jiakuan}, title = {Lower Bounds on the Number of Cyclic Subgroups in Finite Non-Cyclic Nilpotent Groups}, journal = {Journal of Mathematical Study}, year = {2022}, volume = {56}, number = {1}, pages = {93--102}, 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v56n1.23.03}, url = {http://global-sci.org/intro/article_detail/jms/21219.html} }
TY - JOUR T1 - Lower Bounds on the Number of Cyclic Subgroups in Finite Non-Cyclic Nilpotent Groups AU - Meng , Wei AU - Lu , Jiakuan JO - Journal of Mathematical Study VL - 1 SP - 93 EP - 102 PY - 2022 DA - 2022/11 SN - 56 DO - http://doi.org/10.4208/jms.v56n1.23.03 UR - https://global-sci.org/intro/article_detail/jms/21219.html KW - $p$-groups, cyclic subgroups, Nilpotent groups. AB -

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.

Wei Meng & Jiakuan Lu. (2022). Lower Bounds on the Number of Cyclic Subgroups in Finite Non-Cyclic Nilpotent Groups. Journal of Mathematical Study. 56 (1). 93-102. doi:10.4208/jms.v56n1.23.03
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