Prove that the product of two infinite cyclic groups is not infinite cyclic
121810
Prove that the product of two infinite cyclic groups is not infinite cyclic.
142894
Showing that a group of order $pq$ is cyclic if it has normal subgroups of order $p$ and $q$
125668
A proof that BS(1,2) is not polycyclic
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
3104
Prove that a group is infinite and nonabelian.
36040
A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.
132127
Proving a direct product of groups is a group
151619
A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic
82485
Show that the set of non zero rationals is not a cyclic group under multiplication.
39938
Subgroups of a cyclic group and their order.
84198
Step in Proof of Cardinality of Product of two Groups
90239
$\mathbb{Z} \times \mathbb{Z}$ is cyclic.
98155
Free products of cyclic groups
30825
Infinite coproduct of abelian groups
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
104460
When a group is cyclic