query: What are the generators of the Galois group of $x^6-3$ over $\mathbb{Q}$?
positive_passages.docid: 9422
positive_passages.text: Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$
negative_passages.docid: 125469
negative_passages.text: What are the generators of $\mathbb{Z}_9^*$?
negative_passages.docid: 119878
negative_passages.text: "Standard" ways of telling if an irreducible quartic polynomial has Galois group C_4?
negative_passages.docid: 56420
negative_passages.text: Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
negative_passages.docid: 19112
negative_passages.text: Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
negative_passages.docid: 129239
negative_passages.text: Additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity
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: 147968
negative_passages.text: Calculate the Factor Group $(\mathbb{Z}_4 \times \mathbb{Z}_6)/\langle(0,2)\rangle$
negative_passages.docid: 115427
negative_passages.text: Galois group of $\prod_{i=1}^{p-1} (X^2-i)$
negative_passages.docid: 50785
negative_passages.text: Galois group of $x^4-5$
negative_passages.docid: 138501
negative_passages.text: Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
negative_passages.docid: 45302
negative_passages.text: Finding the $\mathbb{Q}$-automorphisms of the splitting field of $x^p-2$ over $\mathbb{Q}$.
negative_passages.docid: 116628
negative_passages.text: Example of Galois extension whose Galois group is $A_4$
negative_passages.docid: 73412
negative_passages.text: Splitting field of $x^6+x^3+1$ over $\mathbb{Q}$
negative_passages.docid: 47522
negative_passages.text: group generators of $(\mathbb Z_{17}-\{0\},\times)$
negative_passages.docid: 115270
negative_passages.text: What are the generators of $(\mathbb{R},+)$?
negative_passages.docid: 63478
negative_passages.text: Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?