showing group $G$ is cyclic if every number $m$ that divides $(G:1)$, there are atmost $m$ elements such that ...
8623
Finite subgroups of the multiplicative group of a field are cyclic
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
151619
A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic
25744
Multiplication in Permutation Groups Written in Cyclic Notation
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
36887
Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.
101596
Determine group G as cyclic
126590
Why is the multiplicative group of a finite field cyclic?
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.
55976
Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?
84501
Proof involving Cyclic group, generator and GCD
147517
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
53207
Let $p$ be a prime. If a group has more than $p − 1$ elements of order $p$, why can’t the group be cyclic?
73211
Cyclic subgroups dealing with prime numbers Question
134820
$p$ prime, Group of order $p^n$ is cyclic iff it is an abelian group having a unique subgroup of order $p$