A characterization of \(F_4(q)\) where \(q=2^n\) (\(n>1\)) (Q2706977)

Let \(G\) be a finite group, its order components were defined by \textit{G. Chen} [J. Algebra 185, No. 1, 184-193 (1996; Zbl 0861.20018)]. In this paper, the authors prove that the simple groups \(F_4(2^n)\) (\(n>1\)) are uniquely determined by their order components. The arguments depend on the prime graph components of simple groups [\textit{J. S. Williams}, J. Algebra 69, 487-513 (1981; Zbl 0471.20013)]. And this theorem is a generalization of a result of the reviewer [\textit{W. Shi}, Pure quantitative characterization of finite simple groups. I. Prog. Nat. Sci. 4, No. 3, 316-326 (1994)].NEWLINENEWLINENEWLINEReviewer's remark: The proof in this paper is not difficult.