Recognition of the group $G_2(5)$ by the prime graph
الموضوعات :
P. Nosratpour
1
(Department of mathematics, ILam Branch, Islamic Azad university, Ilam, Iran)
M. R. Darafsheh
2
(School of Mathematics, statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran)
الکلمات المفتاحية: prime graph, recognition, linear group,
ملخص المقالة :
Let $G$ be a finite group. The prime graph of $G$ is a graph $\Gamma(G)$ with vertex set $\pi(G)$, the set of all prime divisors of $|G|$, and two distinct vertices $p$ and $q$ are adjacent by anedge if $G$ has an element of order $pq$. In this paper we prove that if $\Gamma(G)=\Gamma(G_2(5))$, then $G$has a normal subgroup $N$ such that $\pi(N)\subseteq\{2,3,5\}$ and $G/N\equivG_2(5)$.
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