On Galois groups of prime degree polynomials with complex roots - Oz Ben-Shimol (Algebra and Discrete Mathematics, 2009)
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 prime degree, introduced by A. Bialostocki and T. Shaska.