Characterization of $G_2(q)$, where $2 < q \equiv 1(mod\ 3)$ by order components

Subject Areas : Group theory

P. Nosratpour ¹

1 - Department of Mathematics, Ilam Branch, Islamic Azad University, Ilam, Iran

Received: 2014-07-03 Accepted : 2015-02-20 Published : 2015-04-01

Keywords: prime graph, linear group, order component,

Abstract :

In this paper we will prove that the simple group$G_2(q)$, where $2 < q \equiv 1(mod3)$is recognizable by the set of its order components, also other word we prove that if $G$ is a finite group with $OC(G)=OC(G_2(q))$, then $G$ is isomorphic to $G_2(q)$.

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