Show that the group $G$ is abelian if $G/Z(G)$ is cyclic
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
3907
Abelian quotient group
135188
Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
27905
Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. Prove that $G $ is an abelian group.
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
57421
If $\forall x \in G$ where G is a group $x=x^{-1}$ then how is this group abelian?
68733
If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
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.
26624
Prove that is group is abelian
90332
Prove that that $U(n)$ is an abelian group.
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.
94090
How to show that for any abelian group $G$, $\text{Hom}(\mathbb{Z},G)$ is isomorphic to $G$
107716
Show that $G$ is cyclic