Showing that every subgroup of an abelian group is normal
51359
Prove that every subgroup of an abelian group is a normal subgroup.
57227
Maximal normal $\pi$-subgroups and torsion subgroups
7973
Groups of order $pq$ have a proper normal subgroup
74964
Showing Galois Group is Abelian
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
142413
Normal Subgroups of $SU(n)$
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
49527
Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
11003
Proving that $G/N$ is an abelian group
6134
Some Subgroup of Dihedral Group is Normal
103423
Normal subgroup where G has order prime
28108
Proving the kernel is a normal subgroup.
113936
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
91772
Proving that $A_n$ is the only proper nontrivial normal subgroup of $S_n$, $n\geq 5$
118337
Let $S$ be a normal p-subgroup of a finite group $G$. Prove that $S \subseteq P$ for every Sylow p-subgroup $P$ of $G$
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$