Let $m, n$ be relatively prime and $G, G'$ be cyclic groups of orders $m, n$, respectively. Show that $G \times G'$ is cyclic of order $mn$.
28362
Product of two cyclic groups is cyclic iff their orders are co-prime
15526
Question on groups of order $pq$
104460
When a group is cyclic
144065
Proving $\phi(G)$ is cyclic if $\phi$ : $G \to H$ is group homomorphism and $G$ is cyclic
22301
If $G$ has no proper subgroup, then $G$ is cyclic of prime order
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
141890
$G$ is a Group of order $pq$, if $G$ has exactly one subgroup of order $p$ and another with order $q$, then $G$ is cyclic ($p,q$ are prime)
50762
If $S_n$ has cyclic subgroups of these orders or not?
83654
Order of an element in a finite cyclic group
61379
Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.
45156
Every group of order $35$ is cyclic?
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
38687
Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$
113013
Let $M$ and $N$ be two normal subgroups of $G$. Show that $M \cap N$ is also normal in $G$. Then show that $G/(M \cap N) \cong (G/M) \times (G/N)$
129485
A subgroup of a cyclic group is cyclic - Understanding Proof
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
36887
Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.