$G/Z(G)$ is cyclic then $G$ is abelian where $G$ is a group and $Z(G)$ is the center of the group.
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
45028
How to show that $\langle a \rangle$ is a subgroup of a group $G$, where $a$ is in center of the group $G$
142346
The conditions $a^2b^2=b^2a^2$ and $a^3b^3=b^3a^3$ make the group $G$ abelian?
144258
How to show a group is cyclic?
90239
$\mathbb{Z} \times \mathbb{Z}$ is cyclic.
65900
Show that a finite group with certain automorphism is abelian
57421
If $\forall x \in G$ where G is a group $x=x^{-1}$ then how is this group abelian?
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
125559
In a group $G$, if for all $a,b,c\in G$, $ab=ca\Rightarrow b=c$, then $G$ is abelian
17510
Proving a set is an abelian group.
144065
Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
6153
Suppose that $G$ is a group with the property that for every choice of elements in $G$, $axb=cxd$ implies $ab=cd$. Prove that $G$ is Abelian.
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
27703
an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.
80273
Prove the centralizer of an element in group $G$ is a subgroup of $G$
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.