“School of Mathematics”
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Paper IPM / M / 11468  


Abstract:  
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(F_{4}(q)), where q=2^{n} > 2, then G has a unique nonabelian composition factor isomorphic to F_{4}(q).We also show that if G is a finite group satisfying G = F_{4}(q) and Γ(G) = Γ(F_{4}(q)), where q = 2^{n} > 2, then G ≅ F_{4}(q). As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F_{4}(q) where q = 2^{n} > 2.
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