Proving a group is cyclic
8746
Groups of order $pq$ without using Sylow theorems
76504
Non-trivial cyclic group with unique generator
61394
The product of finitely many cyclic groups is cyclic
104460
When a group is cyclic
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
121810
Prove that the product of two infinite cyclic groups is not infinite cyclic.
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
101596
Determine group G as cyclic
84
For what $n$ is $U_n$ cyclic?
127306
Is the group of units of a finite ring cyclic?
118894
Cyclic subgroup of dihedral group
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
98155
Free products of cyclic groups
84501
Proof involving Cyclic group, generator and GCD
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
112933
Show that $Z\times Z$ is not cyclic...