@article {
author = {Khosravi, Behrooz and Kalantarpour, Cyrus},
title = {The validity of a Thompsonâ€™s problem for $\rm{PSL(4,7)}$},
journal = {AUT Journal of Mathematics and Computing},
volume = {1},
number = {1},
pages = {89-94},
year = {2020},
publisher = {Amirkabir University of Technology},
issn = {2783-2449},
eissn = {2783-2287},
doi = {10.22060/ajmc.2019.16174.1022},
abstract = {Let $\pi_e(G)$ be the set of elements orders of $G$. Also let $s_n$ be the number of elements of order $n$ in $G$ and ${\rm nse}(G)=\{s_n| n\in\pi_e(G)\}$. In this paper we prove that if $G$ is a group such that ${\rm nse}(G)= {\rm nse}(\rm PSL(4,7))$, $19\big\vert|G|$ and $19^2\nmid|G|$, then $G\cong{\rm PSL(4,7)}$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $\rm{PSL(4,7)}$.},
keywords = {Thompsonâ€™s problem,Characterization,Number of elements of the same order,Projective special linear group,Hall subgroup,NSE,Sporadic groups,Python},
url = {https://ajmc.aut.ac.ir/article_3746.html},
eprint = {https://ajmc.aut.ac.ir/article_3746_c15795a34e3e77400bdbc8563d65144d.pdf}
}