On Galois Groups of Prime Degree Polynomials with Complex Roots
| dc.creator | Ben-Shimol, Oz | |
| dc.date | 2007-09-18 | |
| dc.date.accessioned | 2026-07-07T08:30:31Z | |
| dc.date.available | 2026-07-07T08:30:31Z | |
| dc.description | Let $f$ be an irreducible polynomial of prime degree $p\geq 5$ over $\QQ$, with precisely $k$ pairs of complex roots. Using a result of Jens Höchsmann (1999), we show that if $p\geq 4k+1$ then $\Gal(f/\QQ)$ is isomorphic to $A_{p}$ or $S_{p}$. This improves the algorithm for computing the Galois group of an irreducible polynomial of prime degree, introduced by A. Bialostocki and T.Shaska. If such a polynomial $f$ is solvable by radicals then its Galois group is a Frobenius group of degree p. Conversely, any Frobenius group of degree p and of even order, can be realized as the Galois group of an irreducible polynomial of degree $p$ over $\QQ$ having complex roots. | |
| dc.identifier | https://arxiv.org/abs/0709.2868 | |
| dc.identifier | http://arxiv.org/abs/0709.2868 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138260 | |
| dc.subject | Number Theory | |
| dc.subject | Group Theory | |
| dc.title | On Galois Groups of Prime Degree Polynomials with Complex Roots | |
| dc.type | text |