Is it true that any quotient group G/N is abelian if N contains the commutator subgroup?
130792
Commutator of a group
2304
What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
40846
When can a (finite) group be written as the quotient of some other group by its center?
40287
Prove: if $a,b\in G$ commute with probability $>5/8$, then $G$ is abelian
66510
A group is abelian if and only if the center of the group is all the group
5741
Direct product of abelian groups
35913
Abelianization of free group is the free abelian group
78006
What is known about the quotient group $\mathbb{R} / \mathbb{Q}$?
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
71035
Non abelian subgroup of a abelian group.
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
26148
A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian?
1577
Order of nontrivial elements is 2 implies Abelian group
128428
Why is the set of commutators not a subgroup?
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
43783
Abelian group (Commutative group)
26624
Prove that is group is abelian