Showing an Abelian group is cyclic
60858
An abelian group of order 6 has an element of order 6.
143550
Order of product of two elements in an abelian group
25235
Finite abelian groups - direct sum of cyclic subgroup
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
43783
Abelian group (Commutative group)
126893
A group of order 2p (p prime) and other conditions - prove abelian.
106123
Is there a finite abelian group $G$ such that $\textrm{Aut}(G)$ is abelian but $G$ is not cyclic?
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
127306
Is the group of units of a finite ring cyclic?
94090
How to show that for any abelian group $G$, $\text{Hom}(\mathbb{Z},G)$ is isomorphic to $G$
158074
Cyclic group $G$ with generator $ab$.
126590
Why is the multiplicative group of a finite field cyclic?
13734
Show that every group of prime order is cyclic
38853
Cyclic group of prime order
39895
Showing a free abelian group is generated by its basis
65900
Show that a finite group with certain automorphism is abelian
87946
Proving that the unities of a ring form a group under multiplication