The Galois groups of the polynomials \(x^ n+ax^ s+b\). II (Q1820817)
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scientific article; zbMATH DE number 3995826
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Galois groups of the polynomials \(x^ n+ax^ s+b\). II |
scientific article; zbMATH DE number 3995826 |
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The Galois groups of the polynomials \(x^ n+ax^ s+b\). II (English)
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1987
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[For part I, see J. Number Theory 25, 230-238 (1987; Zbl 0608.12010).] This paper gives conditions under which the Galois group of a polynomial \(x^ n+ax^ s+b\) over the rational number field \({\mathbb{Q}}\) is isomorphic to the symmetric group \(S_ n\). Further, this paper gives a criterion for the Galois group of a polynomial over \({\mathbb{Q}}\) to be isomorphic to \(S_ n\) or to \(A_ n\). The author also constructs infinitely many polynomials with the Galois groups \(A_ 4\), \(A_ 5\) and \(A_ 7\).
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prescribed Galois group
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Galois group of polynomial
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symmetric group
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Galois group isomorphic to \(S_ n\)
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Galois group isomorphic to \(A_ n\)
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