A characterization of \(\text{PSL}(3,q)\) where \(q\) is an odd prime power
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)]. The authors prove that \(\text{PSL}(3,q)\) can be uniquely determined by its set of order components where \(q\) is an odd prime power. A main consequence of this result is the validity of Thompson's conjecture [see \textit{W.-J. Shi} and \textit{J.-X. Bi}, Lect. Notes Math. 1456, 171-180 (1990; Zbl 0718.20009)] for the groups under consideration.
scientific article; zbMATH DE number 1758361
scientific article