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Paper   IPM / M / 8548
School of Mathematics
  Title:   Quasirecognition by prime graph of the simple group 2G2(q)
  Author(s):  Behr. Khosravi (Joint with A. Khosravi)
  Status:   Published
  Journal: Siberian Math. J.
  Vol.:  48
  Year:  2007
  Pages:   570-577
  Supported by:  IPM
  Abstract:
Let G be a finite group. The main result of this paper is as follows: If G is a finite group, such that Γ(G) = Γ(2G2(q)), where q = 32n+1 for some n ≥ 1, then G has a (unique) nonabelian composition factor isomorphic to 2G2(q). As a consequence, we prove that if G is a finite group satisfying |G| = |2G2(q)| and Γ(G) = Γ(2G2(q)) then G2G2(q). This enables us to give new proofs for some theorems; e.g., a conjecture of W. Shi and J. Bi. Applications of this result are also considered to the problem of recognition by element orders of finite groups.

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