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 = 2n > 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 = 2n > 2, then \({G \cong F_4(q)}\). As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F 4(q) where q = 2n > 2.
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Communicated by John S. Wilson.
B. Khosravi was supported in part by a grant from IPM (No. 88200038).
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Khosravi, B., Babai, A. Quasirecognition by prime graph of F 4(q) where q = 2n > 2. Monatsh Math 162, 289–296 (2011). https://doi.org/10.1007/s00605-009-0155-6
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DOI: https://doi.org/10.1007/s00605-009-0155-6