University of Isfahan International Journal of Group Theory 2251-7650 11 1 2022 03 01 Characterization of the Chevalley group $G_{2}(5)$ by the set of numbers of the same order elements 7 16 25484 10.22108/ijgt.2021.120906.1594 EN Maryam Jahandideh Department of Mathematics, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran. Mohammad Reza Darafsheh School of Mathematics, Statistics and computer Science, College of Science, University of Tehran, Tehran, Iran. Journal Article 2020 01 04 Let $G$ be a group and $\omega(G)=\{o(g)|g\in G\}$ be the set of element orders of $G$. Let $k\in\omega(G)$ and $s_{k}=|\{g\in G|o(g)=k\}|$. Let $nse(G)=\{s_{k}|k\in\omega(G)\}.$ In this paper, we prove that if $G$ is a group and $G_{2}(5)$ is the Chevalley simple group of type $G_{2}$ over $GF(5)$ such that $nse(G)=nse(G_{2}(5))$, then $G\cong G_{2}(5)$. https://ijgt.ui.ac.ir/article_25484_884d817927f944f400891de68acb7d1f.pdf