On Galois groups of prime degree polynomials with complex roots

• Published in: Algebra and Discrete Mathematics
• Date: 2009
• ISSN: 1726-3255
• Main Author: Oz Ben-Shimol
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154610
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Galois groups of prime degree polynomials with complex roots / Oz Ben-Shimol // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 2. — С. 99–107. — Бібліогр.: 19 назв. — англ.

Let f be an irreducible polynomial of prime degree p≥5 over Q, with precisely k pairs of complex roots. Using a result of Jens Hochsmann (1999), show that if p≥4k+1 then Gal(f/Q) is isomorphic to Ap or Sp. This improves the algorithm for computing the Galois group of an irreducible polynomial of p...