Center of a group contains a normal subgroup
101360
Why is a normal subgroup of $G_1\times G_2$ with trivial intersections with $G_1$ and $G_2$ is abelian?
97751
Center of a group ring?
115204
Show that SO(n) is a normal subgroup of O(n)
72932
Center of Lie group and Lie algebra
2174
Proving that HK is a subgroup when K is normal
123610
How to show that the commutator subgroup is a normal subgroup
158975
Isomorphism of centers of isomorphic groups
12502
The center of a non-Abelian group of order 8
49666
Generalization of index 2 subgroups are normal
113925
Normal Subgroup Counterexample
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
29802
Part of simple proof of nontrivial center in p-group
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
114320
Showing that if the center of a group is trivial, then the center of its automorphism group is trivial
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
23533
All subgroups normal $\implies$ abelian group
155054
$G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then $G=HK$?