P. Nosratpour, M. R. Darafsheh, “Characterization of $G_2(q)$, where $2<q\equiv-1(\mathrm{mod}3)$, by order components”, Sibirsk. Mat. Zh., 2013, Volume 54, Number 5,Pages 1102

This article is cited in 1 paper

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

P. Nosratpour^a, M. R. Darafsheh^b

^a Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
^b School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

Abstract: We prove that the simple group $G_2(q)$, where $2<q\equiv-1(\mathrm{mod}3)$, is recognizable by the set of its order components. In other words, we prove that if $G$ is a finite group with $OC(G)=OC(G_2(q))$, then $G\cong G_2(q)$.

Keywords: prime graph, order component, finite simple groups.

UDC: 512.542

Received: 09.11.2011