query: Galois group is determined by action on roots of polynomial
positive_passages.docid: 28576
positive_passages.text: Galois Groups are isomorphic to subgroups of symmetric groups.
negative_passages.docid: 118916
negative_passages.text: How do I prove that a polynomial F[x] of degree n has at most n roots
negative_passages.docid: 42213
negative_passages.text: Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
negative_passages.docid: 70981
negative_passages.text: Galois Group of $x^5+1$
negative_passages.docid: 99346
negative_passages.text: Prove a result on transitive group actions.
negative_passages.docid: 90273
negative_passages.text: Primitive roots of the unity in $\mathbb C$
negative_passages.docid: 3161
negative_passages.text: Galois group of $x^6 + 3$ isomorphic to a copy of $S_3$ inside $S_6$
negative_passages.docid: 111291
negative_passages.text: Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
negative_passages.docid: 129687
negative_passages.text: Does a Galois group being $S_3$ correspond to the extension being the splitting field of a cubic?
negative_passages.docid: 146312
negative_passages.text: Is the set of roots with respect to their values and multiplicies unique for each $g(x)$ in $a_n x^n + g(x)$?
negative_passages.docid: 130745
negative_passages.text: Action of finite group of automorphisms on Spec A
negative_passages.docid: 8602
negative_passages.text: Galois Group of $(x^2-p_1)\cdots(x^2-p_n)$
negative_passages.docid: 109286
negative_passages.text: Galois group of $x^4-2x^2-2$
negative_passages.docid: 129153
negative_passages.text: Is it Galois extension?
negative_passages.docid: 121707
negative_passages.text: Generating Elements of Galois Group
negative_passages.docid: 137233
negative_passages.text: $f$ is irreducible $\iff$ $G$ act transitively on the roots
negative_passages.docid: 75828
negative_passages.text: Compute Galois group of $\mathbb F_q/\mathbb F_p$