Amirkabir University of TechnologyAUT Journal of Mathematics and Computing1120200201The Validity of a Thompsonâ€™s Problem for PSL(4, 7)8994374610.22060/ajmc.2019.16174.1022ENBehroozKhosraviDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)CyrusKalantarpourDepartment of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, IranJournal Article20190421Let $pi_e(G)$ 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)= lbrace s_nmid nin pi_e(G) rbrace $.<br />In this paper we prove that if $ G$ is a group such that ${rm nse}(G)= {rm nse}(rm PSL(4,7)) $, $19bigvert|G|$ and $19^2nmid|G|$, then $ Gcong rm PSL(4,7)$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $rm PSL(4,7)$.https://ajmc.aut.ac.ir/article_3746_c15795a34e3e77400bdbc8563d65144d.pdf