If both N and G/N are cyclic, then G is cyclic.
75254
Properties possessed by $H , G/H$ but not G
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
57809
For which $n$, $G$ is abelian?
144065
Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
84501
Proof involving Cyclic group, generator and GCD
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
126089
Showing $U(20)$ is not cyclic: Is my proof correct?
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
8623
Finite subgroups of the multiplicative group of a field are cyclic
158074
Cyclic group $G$ with generator $ab$.
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
16673
If $X$ and $Y$ are independent then $f(X)$ and $g(Y)$ are also independent.
129485
A subgroup of a cyclic group is cyclic - Understanding Proof
75986
If all Subgroups are Cyclic, is group Cylic?
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.