query: The Galois Group of $x^4 - 5x^2 + 6$
positive_passages.docid: 95602
positive_passages.text: Computing the Galois group of $x^4+ax^2+b \in \mathbb{Q}[x] $
negative_passages.docid: 50530
negative_passages.text: Finding Galois group of $K=\Bbb{Q}(\omega,\sqrt2)$, showing that $K=\Bbb{Q}(\omega\sqrt2)$, and finding $\operatorname{min}(\omega\sqrt2,\Bbb{Q})$
negative_passages.docid: 81944
negative_passages.text: Galois representations and normal bases
negative_passages.docid: 73713
negative_passages.text: Prove that $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$ is Galois over $\mathbb{Q}$ is Galois and determine the Galois group
negative_passages.docid: 127330
negative_passages.text: Exercises on Galois Theory
negative_passages.docid: 78696
negative_passages.text: Galois group of the product of two fields being the product of Galois groups?
negative_passages.docid: 9422
negative_passages.text: Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$
negative_passages.docid: 103238
negative_passages.text: Conjugates of ${\sqrt 5 + \sqrt 6 }$ over $\mathbb{Q}$ and irreducibility of $x^4 -22x^2+1$ (for minimal polynomial)
negative_passages.docid: 107816
negative_passages.text: Solving a six-degree polynomial of the form $ax^6+bx^3+g$.
negative_passages.docid: 147968
negative_passages.text: Calculate the Factor Group $(\mathbb{Z}_4 \times \mathbb{Z}_6)/\langle(0,2)\rangle$
negative_passages.docid: 19525
negative_passages.text: Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8
negative_passages.docid: 36997
negative_passages.text: Galois Groups of Finite Extensions of Fixed Fields
negative_passages.docid: 147158
negative_passages.text: Galois group of a non-separable polynomial
negative_passages.docid: 622
negative_passages.text: Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
negative_passages.docid: 60858
negative_passages.text: An abelian group of order 6 has an element of order 6.
negative_passages.docid: 9129
negative_passages.text: Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
negative_passages.docid: 56647
negative_passages.text: Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?