Finite abelian groups of order $pq$?
25835
Structure of groups of order $pq$, where $p,q$ are distinct primes.
16476
Order of the product of two commuting elements with coprime orders in a group.
70001
Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)
54453
Finite abelian $p$-group with only one subgroup size $p$ is cyclic
145127
For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
96878
A finite group with the property that all of its proper subgroups are abelian
38853
Cyclic group of prime order
126893
A group of order 2p (p prime) and other conditions - prove abelian.
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
122335
Abelian $p$-group with unique subgroup of index $p$
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
81354
The product of all the elements of a finite abelian group
59211
Product of Finite Abelian Group
68971
Elementary approach to proving that a group of order 9 is Abelian
9393
Order of elements is lcm-closed in abelian groups
113936
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
41731
Question about the order of the product of two elements in an abelian group