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 - <p style="text-align: justify;">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.</p>