On Galois groups of prime degree polynomials with complex roots
Let \(f\) be an irreducible polynomial of prime degree \(p\geq 5\) over \({\mathbb Q}\), with precisely \(k\) pairs of complex roots. Using a result of Jens Hochsmann (1999), show that if \(p\geq 4k+1\) then \(\operatorname{Gal}(f/{\mathbb Q})\) is isomorphic to \(A_{p}\) or \(S_{p}\). This improv...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/780 |
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| Journal Title: | Algebra and Discrete Mathematics |