The \((2,3)\)-generation of the classical simple groups of dimensions \(6\) and \(7\). (Q2786579)
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scientific article; zbMATH DE number 6541564
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \((2,3)\)-generation of the classical simple groups of dimensions \(6\) and \(7\). |
scientific article; zbMATH DE number 6541564 |
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15 February 2016
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\((2,3)\)-generated groups
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classical groups
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finite simple groups
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The \((2,3)\)-generation of the classical simple groups of dimensions \(6\) and \(7\). (English)
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A group is said to be \((2,p)\)-generated if it can be generated by two elements \(X,Y\) of respective orders \(2\) and \(p\), where \(p\) is a prime.NEWLINENEWLINE The author of this paper provides an overview of the research done on the \((2,p)\)-generation of groups. The main result obtained by the author is that the finite simple groups \(\text{PSp}_6(q)\), \(\Omega_7(q)\) and \(\text{PSU}_7(q^2)\) are \((2,3)\)-generated for all \(q\).
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