The group $[G, G]$ generated by the set of all commutators is normal in $G$
38095
The Commutator Subgroup is Normal.
138410
Centralizer of $\mathbb{C}[G]$ in $\mathbb{C}[H]$
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
45277
The alternating group is a normal subgroup of the symmetric group
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
99999
A question on identifying normal subgroups of $S_4$
116936
Commutator subgroup and subgroup generated by square.
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
11731
Normal subgroups of $S_4$
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
7973
Groups of order $pq$ have a proper normal subgroup
68436
Groups in derived series are normal in the whole group
70373
Intersection of normal subgroups proof
43759
Prove that the set $\mathrm{Aut}(G)$ of all automorphisms of the group $G$ with the operation of taking the composition is a group
115204
Show that SO(n) is a normal subgroup of O(n)
47522
group generators of $(\mathbb Z_{17}-\{0\},\times)$
80273
Prove the centralizer of an element in group $G$ is a subgroup of $G$