On Galois groups of prime degree polynomials with complex roots

• Date: 2018
• Main Author: Ben-Shimol, Oz
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: 20B35; 12F12
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/780
• Journal Title: Algebra and Discrete Mathematics

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...