Proving multiplicative group is not cyclic
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
127306
Is the group of units of a finite ring cyclic?
125668
A proof that BS(1,2) is not polycyclic
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
14528
Proof that all abelian simple groups are cyclic groups of prime order
69046
Proof of $\mathbb{Q}$ is not cyclic
92430
Show that the group is cyclic.
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
119545
Nonzero rationals under multiplication are not a cyclic group
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
107716
Show that $G$ is cyclic
145561
About the additive group and the multiplicative group of a field
5223
$\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
34552
Proper subgroups of non-cyclic p-group cannot be all cyclic?
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
129485
A subgroup of a cyclic group is cyclic - Understanding Proof