$\Bbb Q(\sqrt 2)$ and $\Bbb Q(\sqrt 3)$ are not isomorphic
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
48962
Show the two fields are not isomorphic
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
143451
Homomorphism from $(\Bbb Q,+)$ to a finite group
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
90276
Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
83919
How to show $D_3\oplus D_4$ is not isomorphic to $D_{24}$?
108044
Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
47914
Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
6171
Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
107163
Proof that $S_3$ isomorphic to $D_3$