دوره 16، شماره 1 - ( 1-1400 )
جلد 16 شماره 1 صفحات 144-137 |
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Salehi Amiri S S, Khalili Asboei A. Recognition of $L_{2}(q)$ by the Main Supergraph. IJMSI 2021; 16 (1) :137-144
URL: http://ijmsi.ir/article-1-1273-fa.html
URL: http://ijmsi.ir/article-1-1273-fa.html
Recognition of $L_{2}(q)$ by the Main Supergraph. مجله علوم ریاضی و انفورماتیک. 1400; 16 (1) :137-144
چکیده:
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 $L_{2}(q)$.
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 $L_{2}(q)$.
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