OD-characterization of all finite nonabelian simple groups with orders having prime divisors at most 13. (Q483473)

Let \(G\) be a finite group and \(\Gamma(G)\) be its prime graph. The degree pattern \(D(G)\) of \(G\) is defined by \textit{A. R. Moghaddamfar} et al., [Algebra Colloq. 12, No. 3, 431-442 (2005; Zbl 1072.20015)]. We say that \(G\) is \(k\)-fold OD-characterizable if there exist exactly \(k\) non-isomorphic finite groups having the same order and same degree pattern as \(G\) and denote \(h_{\mathrm{OD}}(G)=k\). In this paper, the authors determine \(h_{\mathrm{OD}}(G)\) for every finite nonabelian simple group \(G\) with order having prime divisors at most 13 on the basis of previous results.