Year: 2023
Author: Wei Meng, Jiakuan Lu
Journal of Mathematical Study, Vol. 56 (2023), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v56n1.23.03
Journal of Mathematical Study, Vol. 56 (2023), Iss. 1 : pp. 93–102
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: $p$-groups cyclic subgroups Nilpotent groups.