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Volume 32 • Number 3 • 2009
• Quasirecognition by Prime Graph of 2Dp(3) Where p = 2n + 1 ≥ 5 is a Prime
A. Babai, B. Khosravi and N. Hasani
Abstract. In this paper as the main result, we show that if E1 is a finite group such that E2, where E3, E4 is a prime number, then E1 has a unique non-abelian composition factor isomorphic to E5. We also show that if E1 is a finite group satisfying E6 and E7, then E8 E5. As a consequence of our result we give a new proof for a conjecture of W. J. Shi and J. X. Bi [A characteristic property for each finite projective special linear group, in Groups-Canberra 1989, 171-180, Lecture Notes in Math., 1456, Springer, Berlin] for E5. Application of this result to the problem of recognition of finite simple groups by the set of element orders are also considered.

2000 Mathematics Subject Classification: 20D05, 20D60.

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