Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
157915
Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
151287
Isomorphic abelian groups which are not isomorphic R-modules
2458
Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why?
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
69046
Proof of $\mathbb{Q}$ is not cyclic
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
149973
Showing the following coordinate rings are not isomorphic
90332
Prove that that $U(n)$ is an abelian group.
150207
Non isomorphic subgroups of cyclic groups
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
59995
Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition.
82046
prove that this double transpose $T''$ it's not injective.