id: 05552123
dt: j
an: 05552123
au: Zhang, Liangcai; Shi, Wujie
ti: Noncommuting graph characterization of some simple groups with connected
    prime graphs.
so: Int. Electron. J. Algebra 5, 169-181, electronic only (2009).
py: 2009
pu: Hacettepe University, Ankara
la: EN
cc: 
ut: finite simple groups; noncommuting graphs; projective special linear groups
ci: Zbl 1105.20016; Zbl 1153.20013
li: http://www.ieja.net/papers/2008/V5/12-V5-2009.pdf
ab: 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.
rv: Anatoli Kondrat’ev (Ekaterinburg)