@article {IOPORT.05552123,
    author       = {Zhang, Liangcai and Shi, Wujie},
    title        = {Noncommuting graph characterization of some simple groups with connected prime graphs.},
    year         = {2009},
    journal      = {International Electronic Journal of Algebra (IEJA) [electronic only]},
    volume       = {5},
    issn         = {1306-6048},
    pages        = {169-181, electronic only},
    publisher    = {Hacettepe University, Ankara},
    abstract     = {The noncommuting graph $\nabla(G)$ associated with a nonabelian finite group $G$ is defined as follows: the vertex set of $\nabla(G)$ is $G\setminus Z(G)$, and two vertices are adjacent by an edge whenever they do not commute. {\it A. Abdollahi, S. Akbari} and {\it H. R. Maimani} [J. Algebra 298, No. 2, 468-492 (2006; Zbl 1105.20016)] conjectured that if $M$ is a finite nonabelian simple group and $G$ is a group such that $\nabla(G)\cong\nabla(M)$, then $G\cong M$. Even though this conjecture is known to hold for all simple groups with nonconnected prime graphs and the alternating group $A_{10}$ (see the paper by {\it L.-L. Wang} and {\it W.-J. Shi} [Commun. Algebra 36, No. 2, 523-528 (2008; Zbl 1153.20013)]), it is still unknown for all simple groups. In the present paper, the authors prove that the conjecture is also true for the group $L_4(8)$. They remark that the new method used in this paper also works well in the case of $L_4(4)$, $L_4(7)$, $U_4(7)$, etc.},
    reviewer     = {Anatoli Kondrat'ev (Ekaterinburg)},
    identifier   = {05552123},
}