A prime order group must be cyclic
13734
Show that every group of prime order is cyclic
23885
Structure of a group, $G$, of order $pq$ where $p, q$ are prime.
98601
Any  group of order four is either cyclic or isomorphic to $V$
129061
How to say that any group of order $pqr$ is cyclic with a provided relation between $p$, $q$, $r$, where they are all distinct primes.
32620
Is every group of order $21$ cyclic?
114535
what groups have only elements of prime order?
117206
$|G|$ and $|{\rm Aut}(G)|$ are relatively prime $\Rightarrow$ $G$ should be cyclic?
57887
When are the product of cyclic groups also cyclic?
21079
Why must a field whose a group of units is cyclic be finite?
58397
Every cyclic group with order > 2 has at least 2 distinct generators
45156
Every group of order $35$ is cyclic?
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
129485
A subgroup of a cyclic group is cyclic - Understanding Proof
157841
Existence of a non-abelian group of order $p^n$.
126893
A group of order 2p (p prime) and other conditions - prove abelian.
148904
Groups of order $p^3$
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$