Publications de l'Institut Mathématique, Nouvelle Série Vol. 95[109], pp. 255–266 (2014) 

ON RECOGNITION BY PRIME GRAPH OF THE PROJECTIVE SPECIAL LINEAR GROUP OVER GF(3)Bahman Khosravi, Behnam Khosravi, Hamid Reza Dalili OskoueiDepartment of Mathematics, Faculty of Science, Qom University of Technology, Qom, Iran; Department of Mathematics, Institute For Advanced Studies in Basic Sciences, Zanjan 4513766731, Iran; Shahid Sattari Aeronautical University of Science and Technology, P.O. Box 1384663113, Tehran, IranAbstract: Let $G$ be a finite group. The prime graph of $G$ is denoted by $\Gamma(G)$. We prove that the simple group $\PSL_n(3)$, where $n\geq 9$, is quasirecognizable by prime graph; i.e., if $G$ is a finite group such that $\Gamma(G)=\Gamma(\PSL_n(3))$, then $G$ has a unique nonabelian composition factor isomorphic to $\PSL_n(3)$. Darafsheh proved in 2010 that if $p>3$ is a prime number, then the projective special linear group $\PSL_p(3)$ is at most 2recognizable by spectrum. As a consequence of our result we prove that if $n\geq 9$, then $\PSL_n(3)$ is at most $2$recognizable by spectrum. Keywords: prime graph, simple group, recognition, quasirecognition Classification (MSC2000): 20D05, 20D60; 20D08 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 31 Mar 2014. This page was last modified: 2 Apr 2014.
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