Galois groups of prime degree polynomials with nonreal roots
| dc.creator | Bialostocki, Arie | |
| dc.creator | Shaska, Tanush | |
| dc.date | 2006-01-17 | |
| dc.date.accessioned | 2026-07-07T06:58:59Z | |
| dc.date.available | 2026-07-07T06:58:59Z | |
| dc.description | In the process of computing the Galois group of a prime degree polynomial $f(x)$ over $\mathbb Q$ we suggest a preliminary checking for the existence of non-real roots. If $f(x)$ has non-real roots, then combining a 1871 result of Jordan and the classification of transitive groups of prime degree which follows from CFSG we get that the Galois group of $f(x)$ contains $A_p$ or is one of a short list. Let $f(x)\in \mathbb Q [x] $ be an irreducible polynomial of prime degree $p \geq 5$ and $r=2s$ be the number of non-real roots of $f(x)$. We show that if $s$ satisfies $s (s \log s + 2 \log s + 3) \leq p $ then $Gal (f)= A_p, S_p$. | |
| dc.identifier | https://arxiv.org/abs/math/0601397 | |
| dc.identifier | http://arxiv.org/abs/math/0601397 | |
| dc.identifier | Lect. Notes in Computing, 13, 2005, 243--255 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107579 | |
| dc.subject | Group Theory | |
| dc.title | Galois groups of prime degree polynomials with nonreal roots | |
| dc.type | text |