TY - JOUR T1 - Recognition of $L_{2}(q)$ by the Main Supergraph TT - JF - IJMSI JO - IJMSI VL - 16 IS - 1 UR - http://ijmsi.ir/article-1-1273-en.html Y1 - 2021 SP - 137 EP - 144 KW - Graph KW - Main supergraph KW - Thompson's problem N2 - 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 $L_{2}(q)$. M3 ER -