On subgroups in the special linear group over a division algebra that contain the subgroup of diagonal matrices (Q1369599)
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scientific article; zbMATH DE number 1076650
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On subgroups in the special linear group over a division algebra that contain the subgroup of diagonal matrices |
scientific article; zbMATH DE number 1076650 |
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On subgroups in the special linear group over a division algebra that contain the subgroup of diagonal matrices (English)
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22 February 1998
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Let \(T\) be a division algebra and \(\Gamma=\text{SL}_n(T)\) with \(n\geq 3\). The author proves that, for any subgroup \(H\) of \(\Gamma\) containing all diagonal matrices, there exists a unique \(D\)-net \(\sigma\) such that \(\Gamma(\sigma)\leq H\leq N_\Gamma(\sigma)\) where \(\Gamma(\sigma)\) is the \(D\)-net subgroup corresponding to \(\sigma\).
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special linear groups
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division algebras
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diagonal matrices
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net subgroups
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