Finding the Galois group of $x^n-a$.
9422
Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$
108914
Splitting field of $x^n-a$ contains all $n$ roots of unity
158588
Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
11003
Proving that $G/N$ is an abelian group
117789
Computing Galois Group of $\mathbb{Q}(\sqrt{2},\sqrt{3}):\mathbb{Q}$
126930
Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
48393
Abelian groups of order n.
152630
showing that a group of order 45 is abelian
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
70981
Galois Group of $x^5+1$
9129
Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
49768
If Gal(K,Q) is abelian then |Gal(K,Q)|=n
74318
Find the nilpotents in $\mathbb{Z}_3[x]/(x^2-1)$
157841
Existence of a non-abelian group of order $p^n$.
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$