RT - Journal Article
T1 - Recognition of $L_{2}(q)$ by the Main Supergraph
JF - IJMSI
YR - 2021
JO - IJMSI
VO - 16
IS - 1
UR - http://ijmsi.ir/article-1-1273-en.html
SP - 137
EP - 144
K1 - Graph
K1 - Main supergraph
K1 - Thompson's problem
AB - 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 Thompsonchr('39')s problem holds for the simple group $L_{2}(q)$.
LA eng
UL http://ijmsi.ir/article-1-1273-en.html
M3
ER -