Geodesic
On Recognition by Prime Graph of the Projective Special Linear Group Over GF(3)
Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 255 .

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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 2-recognizable 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.
Classification : 20D05 20D60 20D08
Keywords: prime graph, simple group, recognition, quasirecognition 
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     author = {Bahman Khosravi and Behnam Khosravi and Hamid Reza Dalili Oskouei},
     title = {On {Recognition} by {Prime} {Graph} of the {Projective} {Special} {Linear} {Group} {Over} {GF(3)}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {255 },
     publisher = {mathdoc},
     volume = {_N_S_95},
     number = {109},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a20/}
}
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Bahman Khosravi; Behnam Khosravi; Hamid Reza Dalili Oskouei. On Recognition by Prime Graph of the Projective Special Linear Group Over GF(3). Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 255 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a20/