A group without proper subgroups is a cyclic group
101596
Determine group G as cyclic
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
57887
When are the product of cyclic groups also cyclic?
151025
If G is a group of order n=35, then it is cyclic
2304
What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
92430
Show that the group is cyclic.
109053
Show that a finite cyclic group of order $n$ has exactly one subgroup of order $d$ dividing $n$ and these are all the subgroups it has
8746
Groups of order $pq$ without using Sylow theorems
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
2254
Finite group with isomorphic normal subgroups and non-isomorphic quotients?
106123
Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
128300
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
84823
When is the group of units in $\mathbb{Z}_n$ cyclic?
124150
Faithful representation implies group is cyclic
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
141890
$G$ is a Group of order $pq$, if $G$ has exactly one subgroup of order $p$ and another with order $q$, then $G$ is cyclic ($p,q$ are prime)