Interection of conjugate elements forms a normal subgroup
45580
Intersection of conjugate subgroups is normal
55493
Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
13523
Are normal subgroups transitive?
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
83115
A set of elements in a reduced unity ring
23533
All subgroups normal $\implies$ abelian group
123610
How to show that the commutator subgroup is a normal subgroup
70373
Intersection of normal subgroups proof
7108
Normal subgroup of prime index
43651
Normal subgroups and factor groups
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
48273
If a maximal subgroup is normal, it has prime index
14255
Commutator subgroup and cyclic normal subgroup
22444
Normal subgroups of dihedral groups
19720
A normal subgroup intersects the center of the $p$-group nontrivially
122266
equivalent definition of normal subgroup
63780
to show characteristic subgroup is normal in G