Without using Cauchy's or Sylow theorems ; can we prove that every group of order $65$ is cyclic?
8746
Groups of order $pq$ without using Sylow theorems
117899
At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
126590
Why is the multiplicative group of a finite field cyclic?
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
17077
Prove or disprove: If $H$ and $G/H$ are cyclic, then $G$ is cyclic.
68201
Cyclic group of order $n$
84501
Proof involving Cyclic group, generator and GCD
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
84
For what $n$ is $U_n$ cyclic?
46674
How can I prove that every group of $N = 255$ elements is commutative?
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
58397
Every cyclic group with order > 2 has at least 2 distinct generators
35664
If $x^m=e$ has at most $m$ solutions for any $m\in \mathbb{N}$, then $G$ is cyclic
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
98155
Free products of cyclic groups
151619
A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic