Given a subgroup $H $, find a normal subgroup of $G$ with index less than or equal to $n!$
86336
For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists
154398
Show that H is a subgroup of G
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
58205
$ N $ normal in a finite group $ G $, $ |N| = 5 $ and $ |G| $ odd. Why is $ N \subseteq Z(G) $?
125244
Equivalent definitions of normal subgroups
93596
If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.
86872
normalized subgroup by another subgroup
7973
Groups of order $pq$ have a proper normal subgroup
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
94999
A subgroup with an index of 2 is normal to the group.
64408
Subgroup of $\mathbb{Q}$ with finite index
22477
If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK.
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
142413
Normal Subgroups of $SU(n)$
2174
Proving that HK is a subgroup when K is normal
51747
Showing that the intersection of all subgroups of order $n$ is normal
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal