Proving G/N is simple if N is a normal subgroup of G
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
19458
Finite groups and Normal subgroups - $G$ is a finite group such that $|G|=n$. Let $p$ be the smallest prime such that $p|n$.
115204
Show that SO(n) is a normal subgroup of O(n)
44165
the image of normal subgroups
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
142413
Normal Subgroups of $SU(n)$
51359
Prove that every subgroup of an abelian group is a normal subgroup.
99999
A question on identifying normal subgroups of $S_4$
58251
To show every sylow p-subgroup is normal in G
11957
G is the product of its Sylow subgroups
111375
Normality of subgroups and Sylow groups under homomorphisms...
4883
Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
65037
$H$ is a maximal normal subgroup of $G$ if and only if $G/H$ is simple.
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$