Frobenius \(\mathbb{Q}\)-groups. (Q706349)
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scientific article; zbMATH DE number 2132302
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Frobenius \(\mathbb{Q}\)-groups. |
scientific article; zbMATH DE number 2132302 |
Statements
Frobenius \(\mathbb{Q}\)-groups. (English)
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8 February 2005
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The authors characterise those Frobenius groups whose irreducible complex characters are rational. Such groups have orders \(3^n\cdot 2\) or \(3^{2n}\cdot 8\) with \(n\in\mathbb{N}\) or \(5^2\cdot 8\). They are semidirect products of elementary Abelian groups and a cyclic group of order 2 or the quaternion group of order 8.
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Frobenius kernels
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Clifford theory
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quaternion group
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rational groups
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irreducible complex characters
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