Proving that $\mathbb{Z}_2\times \mathbb{Z}_2$ and $\mathbb{Z}_4$ are not isomorphic
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
40490
Birational isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$
118073
Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
36137
Prove $GL_2(\mathbb{Z}/2\mathbb{Z})$ is isomorphic to $S_3$
53327
$C_2 \times C_2$ and $C_4$
94296
Classifying the factor group $(\mathbb{Z} \times \mathbb{Z})/\langle (2, 2) \rangle$
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
81238
Is $O(2)$ really not isomorphic to $SO(2)\times \{-1,1\}$?
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
23879
If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$
70861
$\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$
47914
Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
1686
Show that quotient rings are not isomorphic
2235
Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
37351
Group of Order $p^2$ Isomorphic to $\mathbb{Z}_{p^2}$ or $\mathbb{Z}_{p}$ $\times$ $\mathbb{Z}_{p}$
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin