Quasirecognition by prime graph of the simple group 2 F 4(q)

Abstract

As the main result, we show that if G is a finite group such that Γ(G) = Γ(2 F 4(q)), where q = 22m+1 for some m 1, then G has a unique nonabelian composition factor isomorphic to 2 F 4(q). We also show that if G is a finite group satisfying |G| =|2 F 4(q)| and Γ(G) = Γ( 2 F 4(q)), then G 2 F 4(q). As a consequence of our result we give a new proof for a conjecture of W. Shi and J. Bi for 2 F 4(q). © 2009 Springer Science+Business Media B.V.