Babai, Azam; Khosravi, Behrooz On the composition factors of a group with the same prime graph as \(B_n(5)\). (English) Zbl 1249.20014 Czech. Math. J. 62, No. 2, 469-486 (2012). Summary: Let \(G\) be a finite group. The prime graph of \(G\) is a graph whose vertex set is the set of prime divisors of \(|G|\) and two distinct primes \(p\) and \(q\) are joined by an edge, whenever \(G\) contains an element of order \(pq\). The prime graph of \(G\) is denoted by \(\Gamma(G)\). It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if \(G\) is a finite group such that \(\Gamma(G)=\Gamma(B_n(5))\), where \(n\geq 6\), then \(G\) has a unique nonabelian composition factor isomorphic to \(B_n(5)\) or \(C_n(5)\). Cited in 3 Documents MSC: 20D06 Simple groups: alternating groups and groups of Lie type 20D60 Arithmetic and combinatorial problems involving abstract finite groups 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:prime graphs; finite simple groups; recognition; quasirecognition; sets of element orders PDFBibTeX XMLCite \textit{A. Babai} and \textit{B. Khosravi}, Czech. Math. J. 62, No. 2, 469--486 (2012; Zbl 1249.20014) Full Text: DOI References: [1] Z. Akhlaghi, M. Khatami, B. Khosravi: Quasirecognition by prime graph of the simple group 2F4(q). Acta Math. Hung. 122 (2009), 387–397. · Zbl 1181.20012 [2] Z. Akhlaghi, B. Khosravi, M. Khatami: Characterization by prime graph of PGL(2, p k) where p and k > 1 are odd. Int. J. Algebra Comput. 20 (2010), 847–873. · Zbl 1216.20006 [3] A. Babai, B. Khosravi, N. Hasani: Quasirecognition by prime graph of 2 D p(3) where p = 2n + 1 5 is a prime. Bull. Malays. Math. Sci. Soc. 32 (2009), 343–350. · Zbl 1172.20015 [4] A. 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