How to prove the diagonal subgroup is a normal subgroup implies that group is abelian?
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
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.
3907
Abelian quotient group
44165
the image of normal subgroups
141125
Group with order $p^2$ must be abelian . How to prove that?
51352
Subgroups of a finite abelian group
26624
Prove that is group is abelian
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
150042
Prove $x^{-1}Hx$ is a subgroup of $G$
45580
Intersection of conjugate subgroups is normal
13631
Showing group with $p^2$ elements is Abelian
123610
How to show that the commutator subgroup is a normal subgroup
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
22444
Normal subgroups of dihedral groups
71420
Prove that a group is abelian.