If an abelian group has subgroups of relatively prime orders r and s(which are cyclic), there exists a subgroup of order rs?
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
48393
Abelian groups of order n.
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
121481
Non-abelian finite $p$-group in which every element has prime order?
61550
Existence of elements of order $p^k$ in a finite group
54195
Do groups of prime order have one subgroup?
39469
If $P \leq G$, $Q\leq G$, are $P\cap Q$ and $P\cup Q$ subgroups of $G$?
122970
A question on $p$-groups, and order of its commutator subgroup.
104080
Group with order $pq$ has subgroups of order $p$ and $q$
71035
Non abelian subgroup of a abelian group.
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
102146
If a group mod its commutator subgroup is cyclic, then the group is abelian?
61379
Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.
114535
what groups have only elements of prime order?
123711
Cyclic group with exactly 3 subgroups: itself $\{e\}$ and one of order $7$. Isn't this impossible?
133770
Subgroups of finite abelian groups.
126113
Prove the existence of order 4 subgroups of order 8 groups