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Paper   IPM / M / 11468
School of Mathematics
  Title:   Quasirecognition by prime graph of F4(q) where q=2n > 2
  Author(s):  Behr. Khosravi (Joint with A. Babai)
  Status:   To Appear
  Journal: Monatsh Math.
  Supported by:  IPM
The prime graph of a finite group G is denoted by Γ(G). In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(F4(q)), where q=2n > 2, then G has a unique nonabelian composition factor isomorphic to F4(q).We also show that if G is a finite group satisfying |G| = |F4(q)| and Γ(G) = Γ(F4(q)), where q = 2n > 2, then GF4(q). As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F4(q) where q = 2n > 2.

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