en عمومى General پژوهشي Research paper Let $G$ be a finite group. The main supergraph $mathcal{S}(G)$ is a graph&nbsp;with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and<br> only if $o(x) mid o(y)$ or $o(y)mid o(x)$. In this paper, we will show&nbsp;that $Gcong L_{2}(q)$ if and only if $mathcal{S}(G)cong mathcal{S}&nbsp;(L_{2}(q))$, where $q$ is a prime power. This work implies that Thompson&#39;s&nbsp;problem holds for the simple group $L_{2}(q)$. Graph, Main supergraph, Thompson's problem 137 144 http://ijmsi.ir/browse.php?a_code=A-10-355-3&slc_lang=en&sid=1 S. S. Salehi Amiri salehisss@baboliau.ac.ir 10031947532846008776 10031947532846008776 No Islamic Azad University, Babol A.R. Khalili Asboei khaliliasbo@yahoo.com 10031947532846008777 10031947532846008777 Yes Farhangian University