Why $O(3)$ does not contain a normal subgroup $\mathbb{Z}/2\mathbb{Z}$?
14666
What are the non-trivial normal subgroups of $O(3)$?
99999
A question on identifying normal subgroups of $S_4$
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
30404
Is $\mathbb{Z}/3\otimes \mathbb{Z}[1/2]=\mathbb{Z}/3$?
156319
Show that a group with $|G| = 33$ contains an element of order $3$
68915
What are the units in $\mathbb{Z}[\root 3 \of 2]$?
133272
Number of normal subgroups of a non abelian group of order $21$... CSIR December $2013$
149578
Subgroups of $(\mathbb Z_n,+)$
109060
Group containing no subgroup of index 2
2235
Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
145511
Suppose $H$ is the only subgroup of order $o(H)$ in the finite group $G$. Prove that $H$ is a normal subgroup of $G$.
57434
$SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong A_4$
75568
Subgroup of index $2$ is Normal
89508
Existence of normal subgroups for a group of order $36$
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
54911
The preimage of a normal subgroup under a group homomorphism is normal
115204
Show that SO(n) is a normal subgroup of O(n)