On the Galois group of \(x^ p + p^ tb(x+1) = 0\) (Q1210371)
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scientific article; zbMATH DE number 179093
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Galois group of \(x^ p + p^ tb(x+1) = 0\) |
scientific article; zbMATH DE number 179093 |
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On the Galois group of \(x^ p + p^ tb(x+1) = 0\) (English)
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11 August 1993
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The author considers polynomials of the form \(f(x)=x^ p+ a(x+1)\) over \(\mathbb{Q}\) when \(p\) is prime and \(p\) divides \(a\), and obtains conditions on \(a\) which imply that the Galois group \(G\) of \(f(x)\) is the symmetric group \(S_ p\). The technical difficulty arises in showing that \(G\) contains a transposition.
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polynomials
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Galois group
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symmetric group
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