If groups have order $3,4$ then they are abelian
74586
Prove that every group of order $4$ is abelian
127603
If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$
66510
A group is abelian if and only if the center of the group is all the group
4838
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
134455
Any group of order $15$ is abelian(without sylow theorem)
48393
Abelian groups of order n.
2731
Groups of even order have an element whose order is 2.
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
65926
Group of order $1575$ having a normal sylow $3$ subgroup is abelian.
108425
Problem on abelian group
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
156429
If $G$ is a group whereby $(a\cdot b)^{i} =a^i\cdot b^i$ for three consecutive integers $i$ for all $a, b \in G$, show $G$ is abelian.
43783
Abelian group (Commutative group)
87882
If $N \lhd G$ is abelian and $G/N$ is abelian then $G$ is abelian
76943
Existence of subgroup of order six in $A_4$
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.