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 -