Given $G$ is cyclic and $H \subset G$, is it true that $G/H$ is a cyclic group?
98145
If $G$ is cyclic then $G/H$ is cyclic?
45727
If $G$ contains a normal subgroup $H \cong \mathbb{Z_2}$ such that $G/H$ is infinite cyclic, then $G \cong \mathbb{Z} \times \mathbb{Z_2}$
61394
The product of finitely many cyclic groups is cyclic
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
28362
Product of two cyclic groups is cyclic iff their orders are co-prime
158873
Is every group the unit group of some ring?
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
53207
Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
57887
When are the product of cyclic groups also cyclic?
46355
If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?
154398
Show that H is a subgroup of G
18361
Does the unit generate the additive group in a unital ring with cyclic additive group?
101596
Determine group G as cyclic
22301
If $G$ has no proper subgroup, then $G$ is cyclic of prime order