A characterization of \(\text{PSU}_3(q)\) for \(q>5\) (Q1864521)

Let \(G\) be a finite group and \(OC(G)\) the set of order components of \(G\) [\textit{G.-Y. Chen}, J. Algebra 185, No. 1, 184-193 (1996; Zbl 0861.20018)]. In this paper the authors prove that \(\text{PSU}(3,q)\) where \(q>5\) can be uniquely determined by its set of order components. A main consequence (Corollary 3.2) of this result is the validity of Thompson's conjecture for the groups under consideration. Corollary 3.4 is proved for the general case of finite unitary groups of any dimension by reviewer and \textit{H.-P. Cao} [Pure quantitative characterization of finite projective special unitary groups, Sci. China, Ser. A 45, No. 6, 761-772 (2002)].