A characterization of \(\text{PSL}(3,q)\) where \(q\) is an odd prime power (Q1602671)
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scientific article; zbMATH DE number 1758361
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of \(\text{PSL}(3,q)\) where \(q\) is an odd prime power |
scientific article; zbMATH DE number 1758361 |
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A characterization of \(\text{PSL}(3,q)\) where \(q\) is an odd prime power (English)
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24 June 2002
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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.
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simple groups of Lie type
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order components
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prime graphs
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conjugacy classes
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