Galois groups of certain even octic polynomials
| Autor: | Malcolm Hoong Wai Chen, Angelina Yan Mui Chin, Ta Sheng Tan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Popis: | Let $f(x)=x^8+ax^4+b \in \mathbb{Q}[x]$ be an irreducible polynomial where $b$ is a square. We give a method that completely describes the factorization patterns of a linear resolvent of $f(x)$ using simple arithmetic conditions on $a$ and $b$. As a result, we determine the exact six possible Galois groups of $f(x)$ and completely classify all of them. As an application, we characterize the Galois groups of irreducible polynomials $x^8+ax^4+1 \in \mathbb{Q}[x]$. We also use similar methods to obtain analogous results for the Galois groups of irreducible polynomials $x^8+ax^6+bx^4+ax^2+1 \in \mathbb{Q}[x]$. 22 pages, preprint of article accepted to Journal of Algebra and Its Applications |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|