@article {
author = {Jahandideh, Maryam and Darafsheh, Mohammad Reza},
title = {Characterization of the Chevalley group $G_{2}(5)$ by the set of numbers of the same order elements},
journal = {International Journal of Group Theory},
volume = {11},
number = {1},
pages = {7-16},
year = {2022},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2021.120906.1594},
abstract = {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 $G\cong G_{2}(5)$.},
keywords = {Element order,Thompson's problem,Number of the same order elements},
url = {https://ijgt.ui.ac.ir/article_25484.html},
eprint = {https://ijgt.ui.ac.ir/article_25484_884d817927f944f400891de68acb7d1f.pdf}
}