The Galois group of random elements of linear groups (Q2927717)
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scientific article; zbMATH DE number 6365642
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Galois group of random elements of linear groups |
scientific article; zbMATH DE number 6365642 |
Statements
The Galois group of random elements of linear groups (English)
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4 November 2014
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Galois group
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linear group
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random elements
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Zariski closure
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From authors' abstract: ``Let \(F\) be a finitely generated field of characteristic zero and \(\Gamma \leq \mathrm{GL} _n (F)\) a finitely generated subgroup. For \(\gamma \in \Gamma \), let \(\mathrm{Gal} (F(\gamma)/F\)) be the Galois group of the splitting field of the characteristic polynomial of \(\gamma\) over \(F\). We show that the structure of \(\mathrm{Gal} (F(\gamma)/F\)) has a typical behavior depending on \(F\) and the geometry of the Zariski closure of \(\Gamma \) (but not on \(\Gamma \)). ''NEWLINENEWLINENEWLINE The symbol \({\mathbb F}\) is used in the paper for a general field.
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