Nosratpour, P., Darafsheh, M. (2012). Recognition of the group $G_2(5)$ by the prime graph. Journal of Linear and Topological Algebra (JLTA), 01(02), 115-120.

P. Nosratpour; M. R. Darafsheh. "Recognition of the group $G_2(5)$ by the prime graph". Journal of Linear and Topological Algebra (JLTA), 01, 02, 2012, 115-120.

Nosratpour, P., Darafsheh, M. (2012). 'Recognition of the group $G_2(5)$ by the prime graph', Journal of Linear and Topological Algebra (JLTA), 01(02), pp. 115-120.

Nosratpour, P., Darafsheh, M. Recognition of the group $G_2(5)$ by the prime graph. Journal of Linear and Topological Algebra (JLTA), 2012; 01(02): 115-120.

Recognition of the group $G_2(5)$ by the prime graph

^{1}Department of mathematics, ILam Branch, Islamic Azad university, Ilam, Iran

^{2}School of Mathematics, statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

Abstract

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 an edge 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 $G/N\equiv G_2(5)$.

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