The multiplicative groups $\mathbb{Q}^\ast$ and $\mathbb{R}^\ast$ are not isomorphic
51334
Does there exist any surjective group homomorphism from $(\mathbb R^* , .)$ onto $(\mathbb Q^* , .)$?
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
149973
Showing the following coordinate rings are not isomorphic
41572
$G/Z$ cannot be isomorphic to quaternion group
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
51861
$S_4$ is not isomorphic to $D_{12}$
108044
Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
8694
$A_4$ is not isomorphic to $D_6$
69046
Proof of $\mathbb{Q}$ is not cyclic
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
80849
There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)