Weakly commensurable \(S\)-arithmetic subgroups in almost simple algebraic groups of types B and C. (Q380358)
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scientific article; zbMATH DE number 6226665
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weakly commensurable \(S\)-arithmetic subgroups in almost simple algebraic groups of types B and C. |
scientific article; zbMATH DE number 6226665 |
Statements
Weakly commensurable \(S\)-arithmetic subgroups in almost simple algebraic groups of types B and C. (English)
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13 November 2013
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Let \(G_1\) and \(G_2\) be absolutely almost simple algebraic groups of types B\(_l\) and C\(_l\), respectively, defined over a number field \(K\). The authors determine when \(G_1\) and \(G_2\) have the same isomorphism or isogeny classes of maximal \(K\)-tori. This leads to necessary and sufficient conditions for two Zariski-dense \(S\)-arithmetic subgroups of \(G_1\) and \(G_2\) to be weakly commensurable.
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simple algebraic groups
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isogenous maximal tori
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weak commensurability
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isomorphic maximal tori
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Zariski-dense \(S\)-arithmetic subgroups
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