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Weidong Xu, Rulin Shen, Almost simple groups with more than one half of the number of cyclic subgroups, Eur. J. Math. Appl. 3 (2023), Article ID 25.

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Volume 3 (2023), Article ID 25

https://doi.org/10.28919/ejma.2023.3.25

Published: 19/12/2023

Abstract:

Let $G$ be a finite group, $c(G)$ the number of cyclic subgroups of $G$, and $\alpha(G)$ the ratio of the number of cyclic subgroups of $G$ to the order of the group, i.e.$\alpha\left(G\right)=c(G)/|G|$. A group $G$ called an almost simple group if there exists a finite non-abelian simple group such that $S\le G\le Aut(S)$. In this paper, we prove that if $G$ is an almost simple group, then $\alpha(G)\ge 1/2$ if and only if $G\cong A_{5},S_{5},S_{6}$.

How to Cite:

Weidong Xu, Rulin Shen, Almost simple groups with more than one half of the number of cyclic subgroups, Eur. J. Math. Appl. 3 (2023), Article ID 25. https://doi.org/10.28919/ejma.2023.3.25