Galois stability for integral representations of finite groups (Q2736046)
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scientific article; zbMATH DE number 1638027
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Galois stability for integral representations of finite groups |
scientific article; zbMATH DE number 1638027 |
Statements
30 June 2002
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algebraic number fields
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algebraic integers
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Galois groups
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integral matrices
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representations of finite groups
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Galois stability for integral representations of finite groups (English)
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Let \(E/F\) be a Galois extension of number fields with Galois group \(\Gamma\), \(R\subset E\) a Dedekind ring (or \(E\) itself), and \(G\subset\text{GL}_n(R)\) a finite \(\Gamma\)-stable subgroup. In the paper the following question is considered: what kind of restrictions on the field \(E\) are implied by the \(\Gamma\)-stability of \(G\), and for which \(F\) can one expect \(G\subset\text{GL}_n(F)\)?
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