Is the commutator subgroup of the commutator subgroup still a normal subgroup?
68436
Groups in derived series are normal in the whole group
92493
If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$
90511
Commutator subgroup of a dihedral group.
102146
If a group mod its commutator subgroup is cyclic, then the group is abelian?
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
113925
Normal Subgroup Counterexample
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
101360
Why is a normal subgroup of $G_1\times G_2$ with trivial intersections with $G_1$ and $G_2$ is abelian?
22477
If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
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 $G$
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
70373
Intersection of normal subgroups proof
51747
Showing that the intersection of all subgroups of order $n$ is normal
141265
Finding a normal and not normal subgroup of $S_3$
5024
Why do we define quotient groups for normal subgroups only?
123677
Normal subgroups of infinite symmetric group
97928
Normal subgroup of a normal subgroup