query: Why does it make sense to talk about the Galois group of this polynomial?
positive_passages.docid: 147158
positive_passages.text: Galois group of a non-separable polynomial
negative_passages.docid: 68733
negative_passages.text: If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
negative_passages.docid: 75828
negative_passages.text: Compute Galois group of $\mathbb F_q/\mathbb F_p$
negative_passages.docid: 86957
negative_passages.text: Galois group of irreducible cubic equation
negative_passages.docid: 12524
negative_passages.text: Galois group of $x^3 - 2 $ over $\mathbb Q$
negative_passages.docid: 26069
negative_passages.text: Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
negative_passages.docid: 112677
negative_passages.text: understanding the commutator of dihedral group
negative_passages.docid: 7530
negative_passages.text: Why this $\sigma \pi \sigma^{-1}$ keeps appearing in my group theory book? (cycle decomposition)
negative_passages.docid: 4048
negative_passages.text: Find the Galois group of $x^3-5$ over $\mathbb{Q}$.
negative_passages.docid: 31831
negative_passages.text: Why every polynomial over the algebraic numbers $F$ splits over $F$?
negative_passages.docid: 74964
negative_passages.text: Showing Galois Group is Abelian
negative_passages.docid: 106101
negative_passages.text: Why there is much interest in the study of $\operatorname{Gal}\left(\overline{\mathbb Q}/\mathbb Q\right)$?
negative_passages.docid: 49338
negative_passages.text: Is every group a Galois group?
negative_passages.docid: 158063
negative_passages.text: A formula for the roots of a solvable polynomial
negative_passages.docid: 70981
negative_passages.text: Galois Group of $x^5+1$
negative_passages.docid: 41069
negative_passages.text: Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
negative_passages.docid: 127330
negative_passages.text: Exercises on Galois Theory