Quasirecognition by prime graph of F₄(q) where q = 2ⁿ > 2

چکیده مقاله

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 {pipe}G{pipe} = {pipe}F₄(q){pipe} and Γ(G) = Γ(F₄(q)), where q = 2ⁿ > 2, then G ≅ F₄(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. © 2009 Springer-Verlag.