query: Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
positive_passages.docid: 56647
positive_passages.text: Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?
negative_passages.docid: 93169
negative_passages.text: Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
negative_passages.docid: 91622
negative_passages.text: Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
negative_passages.docid: 28934
negative_passages.text: Presentation of SL$(n,\mathbb{Z}_p)$
negative_passages.docid: 95563
negative_passages.text: Galois group of a biquadratic quartic
negative_passages.docid: 132725
negative_passages.text: Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
negative_passages.docid: 86877
negative_passages.text: Let $F$ be a Galois extension over $\mathbb{Q}$ with $[F:\mathbb{Q}]=2^n$, then all elements in $F$ are constructible
negative_passages.docid: 8602
negative_passages.text: Galois Group of $(x^2-p_1)\cdots(x^2-p_n)$
negative_passages.docid: 103148
negative_passages.text: Show Galois group of $f(t) = t^5 - 3$ over $\mathbb Q$ is solvable
negative_passages.docid: 109596
negative_passages.text: Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
negative_passages.docid: 157915
negative_passages.text: Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
negative_passages.docid: 118299
negative_passages.text: Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
negative_passages.docid: 78852
negative_passages.text: If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
negative_passages.docid: 49768
negative_passages.text: If Gal(K,Q) is abelian then |Gal(K,Q)|=n
negative_passages.docid: 98256
negative_passages.text: Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
negative_passages.docid: 85752
negative_passages.text: Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
negative_passages.docid: 622
negative_passages.text: Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$