normality of subgroup of odd prime index
7108
Normal subgroup of prime index
112263
an example for $\pi$-quasinormal subgroup but is not normal
63780
to show characteristic subgroup is normal in G
138108
If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$.
7528
Index of the center of a group in the group is not a prime number
157819
Every group of order $56$ has a proper non - trivial normal subgroup?
55178
When there is a unique Sylow p-subgroup it is normal, does this mean that non-unique p-subgroups are not normal?
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
104505
Is every normal subgroup the kernel of some endomorphism?
37971
Prove that the center of a group is a normal subgroup
13523
Are normal subgroups transitive?
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
21152
Exactly half of the elements of $\mathcal{P}(A)$ are odd-sized
125244
Equivalent definitions of normal subgroups
75568
Subgroup of index $2$ is Normal
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$