Every group of order $14077=7 \cdot 2011$ is cyclic (use Sylow Theorem)
25835
Structure of groups of order $pq$, where $p,q$ are distinct primes.
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
119808
Proving that $n$-cycle has order $n$
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
90329
Prove there is no simple group of order $729$
46940
On Groups of Order 315 with a unique sylow 3-subgroup .
82878
Order of cyclic groups and the Euler phi function
74586
Prove that every group of order $4$ is abelian
65968
Prove that any two cyclic groups of the same order are isomorphic?
11957
G is the product of its Sylow subgroups
15706
"Every Group of order $216$ contains a normal subgroup of order $27$ or $9$
123711
Cyclic group with exactly 3 subgroups: itself $\{e\}$ and one of order $7$. Isn't this impossible?
152630
showing that a group of order 45 is abelian
28362
Product of two cyclic groups is cyclic iff their orders are co-prime
32620
Is every group of order $21$ cyclic?
155219
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic