Some finite simple groups which are not uniquely determined by their order components.
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 the projective symplectic groups \(S_{16}(q)\), where \(q\) is an odd prime power, are not uniquely determined by their order components. But \(S_{16}(q)\), where \(q=2^n\), are uniquely determined by their order components.
scientific article; zbMATH DE number 2148370