Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 2, pp. 443448 (2009) 

Characterization of $\mathrm{SL}(2,q)$ by its noncommuting graphAlireza AbdollahiDepartment of Mathematics, University of Isfahan, Isfahan 8174673441, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran email: abdollahi@member.ams.orgAbstract: Let $G$ be a nonabelian group and $Z(G)$ be its center. The noncommuting graph $\mathcal{A}_G$ of $G$ is the graph whose vertex set is $G\backslash Z(G)$ and two vertices are joined by an edge if they do not commute. Let $\mathrm{SL}(2,q)$ be the special linear group of degree 2 over the finite field of order $q$. In this paper we prove that if $G$ is a group such that $\mathcal{A}_G\cong \mathcal{A}_{\mathrm{SL}(2,q)}$ for some prime power $q\geq 2$, then $G\cong \mathrm{SL}(2,q)$. Keywords: noncommuting graph, general linear group, special linear group Classification (MSC2000): 20D60 Full text of the article:
Electronic version published on: 28 Aug 2009. This page was last modified: 28 Jan 2013.
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