Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
40993
Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
14255
Commutator subgroup and cyclic normal subgroup
144065
Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
144258
How to show a group is cyclic?
71420
Prove that a group is abelian.
81040
proof about commutative operators and T-cyclic vectors
43783
Abelian group (Commutative group)
124150
Faithful representation implies group is cyclic
158074
Cyclic group $G$ with generator $ab$.
84501
Proof involving Cyclic group, generator and GCD
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
151025
If G is a group of order n=35, then it is cyclic
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is 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.
61394
The product of finitely many cyclic groups is cyclic