International Journal of Nonlinear Analysis and Applications

A nilpotency criterion for finite groups by the sum of element orders

Document Type : Research Paper

Authors

1 Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran

2 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran

Abstract

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.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 1
January 2023
Pages 2931-2937
  • Receive Date: 14 May 2022
  • Revise Date: 02 July 2022
  • Accept Date: 24 July 2022