Why if $(\mathbf B, \cdot)$ is a finite order group with prime order then $(\mathbf B, \cdot)$ is cyclic?
13734
Show that every group of prime order is cyclic
2104
Finite group for which $|\{x:x^m=e\}|\leq m$ for all $m$ is cyclic.
65968
Prove that any two cyclic groups of the same order are isomorphic?
31511
A finite abelian group that does not contain a subgroup isomorphic to $\mathbb Z_p\oplus\mathbb Z_p$, for any prime $p$, is cyclic.
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
126590
Why is the multiplicative group of a finite field cyclic?
68201
Cyclic group of order $n$
106123
Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
73211
Cyclic subgroups dealing with prime numbers Question
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
40993
Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
68733
If $G/Z(G)$ is cyclic then $G$ is abelian – what is the point?
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
117899
At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic
117206
$|G|$ and $|{\rm Aut}(G)|$ are relatively prime $\Rightarrow$ $G$ should be cyclic?
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
84823
When is the group of units in $\mathbb{Z}_n$ cyclic?