If N is a subgroup normal of the group G such that $N \cap G'=\{e_{G}\}$, show that $N \subset Z(G).$
104855
Prove that $N \subset Z(G)$
80186
How to show that $K\leq S_4$ is a normal subgroup?
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
8841
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
123610
How to show that the commutator subgroup is a normal subgroup
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 $G=HK$?
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
2761
If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$.
44934
Show that every normal subgroup can be written as an intersection of $\ker \chi$'s for $\chi \in \operatorname{Irr}(G).$
138406
If N and every subgroup of N is normal in G then G/N is abelian .
109236
Subgroups containing kernel of group morphism to an abelian group are normal.
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
142413
Normal Subgroups of $SU(n)$
51359
Prove that every subgroup of an abelian group is a normal subgroup.
28108
Proving the kernel is a normal subgroup.
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$