Normal subgroups and abelian groups
23533
All subgroups normal $\implies$ abelian group
63780
to show characteristic subgroup is normal in G
113925
Normal Subgroup Counterexample
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
70373
Intersection of normal subgroups proof
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
101079
Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$
142413
Normal Subgroups of $SU(n)$
44165
the image of normal subgroups
7973
Groups of order $pq$ have a proper normal subgroup
5741
Direct product of abelian groups
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
61373
A normal subgroup that is not a characteristic
102622
K is a subgroup of G. Show that K is not a normal subgroup
49666
Generalization of index 2 subgroups are normal
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
47731
Intersection of all $p$-Sylow subgroups is normal