%0 Journal Article %A Salehi Amiri, S. S. %A Khalili Asboei, A.R. %T Recognition of $L_{2}(q)$ by the Main Supergraph %J Iranian Journal of Mathematical Sciences and Informatics %V 16 %N 1 %U http://ijmsi.ir/article-1-1273-en.html %R %D 2021 %K Graph, Main supergraph, Thompson's problem, %X Let $G$ be a finite group. The main supergraph $mathcal{S}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) mid o(y)$ or $o(y)mid o(x)$. In this paper, we will show that $Gcong L_{2}(q)$ if and only if $mathcal{S}(G)cong mathcal{S} (L_{2}(q))$, where $q$ is a prime power. This work implies that Thompson's problem holds for the simple group $L_{2}(q)$. %> http://ijmsi.ir/article-1-1273-en.pdf %P 137-144 %& 137 %! %9 Research paper %L A-10-355-3 %+ Farhangian University %G eng %@ 1735-4463 %[ 2021