Show that a certain group is normal
4883
Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
49666
Generalization of index 2 subgroups are normal
6134
Some Subgroup of Dihedral Group is Normal
156319
Show that a group with $|G| = 33$ contains an element of order $3$
25832
Let $K$ be a normal subgroup of order 2 in group $G$, show that $K$ lies in the centre of $G$
43913
Prove that if $A^*+A=AA^*$ then $A$ is normal
113413
How do I show that two groups are not isomorphic?
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
133298
Assume $|G|=40$. Show that the subgroup of order $8$ is normal and unique.
23533
All subgroups normal $\implies$ abelian group
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
68436
Groups in derived series are normal in the whole group
71420
Prove that a group is abelian.
89508
Existence of normal subgroups for a group of order $36$