A determination of the automorphisms of certain algebraic fields (Q2646034)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A determination of the automorphisms of certain algebraic fields |
scientific article |
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A determination of the automorphisms of certain algebraic fields (English)
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1938
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The author determines explicitly the automorphisms of all normal fields of degree \(n=3, 4, 6\) in terms of the coefficients of the defining equations. Similarly for all abelian fields of degree 8 and type \((2, 2, 2)\) or \((2, 4)\) and for a one-parameter family of cyclic octics. The method is purely rational. At the same time rational parametric representations of the most general equations defining these fields are obtained.
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automorphisms
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normal fields
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purely algebraic method
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cyclic cubic
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quartic
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sextic
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quartic with four-group
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sextic with symmetric group
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octics with abelian groups of type \((2, 2, 2)\) or \((2, 4)\)
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parametric representations
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