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Paper   IPM / M / 8311
School of Mathematics
  Title:   Groups with the same prime graph as a CIT simple group
  Author(s):  Behr. khosravi (Joint with Behn. Khosravi and Bah. Khosravi)
  Status:   Published
  Journal: Houston J. Math.
  Vol.:  33
  Year:  2007
  Pages:   967-977
  Supported by:  IPM
Let G be a finite group. We denote by Γ(G) the prime graph of G. Recently M. Hagie in (Hagie, M. (2003), The prime graph of a sporadic simple group, Comm. Algebra, 31: 4405-4424) determined finite groups G satisfying Γ(G) = Γ(S), where S is a sporadic simple group. We called M a CIT group if M is of even order and the centralizer of any involution is a 2-group. In this paper we determine finite groups G such that Γ(G) = Γ(M) where M is a CIT simple group. In fact we prove that if Γ(G) = Γ(PSL(2,p)) and p > 7 is a Mersenne prime, then GPSL(2,p). As a consequence of our results we can give positive answer to a conjecture of W. Shi and J. Bi.

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