Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
38687
Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
69046
Proof of $\mathbb{Q}$ is not cyclic
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
18160
How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
51695
Finding all homomorphisms between $\mathbb{Z}/m\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$
32516
show that rational numbers with the multipiciation are not abelian finitely generated group
13631
Showing group with $p^2$ elements is Abelian
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
23879
If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$