Cyclic $G/Z(G)$ implies that $G$ is abelian
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
61394
The product of finitely many cyclic groups is cyclic
43783
Abelian group (Commutative group)
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.
132725
Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
20679
Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
104855
Prove that $N \subset Z(G)$
74964
Showing Galois Group is Abelian
25235
Finite abelian groups - direct sum of cyclic subgroup
17077
Prove or disprove: If $H$ and $G/H$ are cyclic, then $G$ 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.
135188
Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
138406
If N and every subgroup of N is normal in G then G/N is abelian .