Normal subgroup intersection with center of p-group is not trivial
19720
A normal subgroup intersects the center of the $p$-group nontrivially
158975
Isomorphism of centers of isomorphic groups
51747
Showing that the intersection of all subgroups of order $n$ is normal
49666
Generalization of index 2 subgroups are normal
43651
Normal subgroups and factor groups
114320
Showing that if the center of a group is trivial, then the center of its automorphism group is trivial
70373
Intersection of normal subgroups proof
117744
$p$-Sylow in quotient groups
6134
Some Subgroup of Dihedral Group is Normal
29802
Part of simple proof of nontrivial center in p-group
144788
Cosets of a subgroup do not overlap
11731
Normal subgroups of $S_4$
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
15630
Normal subgroup of prime order is characteristic
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
11393
The center of the dihedral group
86872
normalized subgroup by another subgroup