Recognition of $L_{2}(q)$ by the Main Supergraph

Author(s):

S. S. Salehi Amiri , A.R. Khalili Asboei*

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

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 $L_{2}(q)$.

Keywords:

Graph , Main supergraph , Thompson's problem

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:16 Issue: 1, May 2021
Pages:
137 to 144
https://www.magiran.com/p2262246  
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