Is $(\Bbb{Q},+)$ isomorphic to $(\Bbb{Q}_{>0},\cdot)$?
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
73790
Are two Hilbert spaces with the same algebraic dimension (their Hamel bases have the same cardinality) isomorphic?
116594
Finite fields are isomorphic
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
137711
Alternative proof that $[\Bbb{Q}(\zeta_n) : \Bbb{Q} ]= \varphi(n)$ uses circular reasoning?
155669
$\mathrm{Aut}(D_4)$ is isomorphic to $D_4$
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
90433
Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
157597
Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
47914
Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
78118
Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
133612
How many isomorphisms are there from $\Bbb Z_{12}$ to $\Bbb Z_{4} \oplus \Bbb Z_{3}$?
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
94579
$\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
150064
Cardinality of "$x-y\in\Bbb Q$"-equivalence class of $1/\sqrt2$
33233
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.