%0 Journal Article %T The validity of a Thompson’s problem for $\rm{PSL(4,7)}$ %J AUT Journal of Mathematics and Computing %I Amirkabir University of Technology %Z 2783-2449 %A Khosravi, Behrooz %A Kalantarpour, Cyrus %D 2020 %\ 02/01/2020 %V 1 %N 1 %P 89-94 %! The validity of a Thompson’s problem for $\rm{PSL(4,7)}$ %K Thompson’s problem %K Characterization %K Number of elements of the same order %K Projective special linear group %K Hall subgroup %K NSE %K Sporadic groups %K Python %R 10.22060/ajmc.2019.16174.1022 %X 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 $\rm{PSL(4,7)}$. %U https://ajmc.aut.ac.ir/article_3746_c15795a34e3e77400bdbc8563d65144d.pdf