Does anyone have a source for a proof on $(\mathbb{C}, +)$ and $(\mathbb{R}, +)$ being isomorphic?
67374
Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
48419
Difference between $\mathbb{R}$-linear and $\mathbb{C}$-linear maps
116168
Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$?
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
36142
What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?
82474
Isometries of $\mathbb{R}^n$
132653
How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
9140
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
146356
To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
90433
Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
107687
How to prove that $U_{2^n}$ is isomorphic as group to $\mathbb Z_2 \times \mathbb Z_{2^{n-2}}$ for $n \ge 3$?
121449
An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$
42810
Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
145000
Fundamental group of GL(n,C) is isomorphic to Z. How to learn to prove facts like this?
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.