$G$ is a cyclic group of order $n$ and there is an integer $m$ that divides $n$.Prove that there is a subgroup of $G$ of order $\frac{n}{m}$.
14890
Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
17178
Order of $\phi(g)$ divides the order of $g$
23885
Structure of a group, $G$, of order $pq$ where $p, q$ are prime.
53357
Cyclic Group Generators of Order $n$
106653
How many generator has a cyclic group of order n?
61379
Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
11003
Proving that $G/N$ is an abelian group
101596
Determine group G as cyclic
126113
Prove the existence of order 4 subgroups of order 8 groups
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
146760
Prove that H is a subgroup of G
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
154398
Show that H is a subgroup of G
107716
Show that $G$ is cyclic