A nilpotency criterion for finite groups by the sum of element orders
نویسندگان
1 Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran
2 Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran
3 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
4 Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran
doi
10.22075/ijnaa.2022.27803.3719چکیده
Let $G$ be a finite group and $\psi(G)=\sum_{g\in G}o(g)$, where $o(g)$ denotes the order of $g\in G$. We give a criterion for nilpotency of finite groups $G$ based on the sum of element orders of $G$. We prove that if $\psi(G)>\frac{13}{21}\psi(C_n)$ then $G$ is a nilpotent group.
