Proving without Zorn's Lemma: additive group of the reals is isomorphic to the additive group of the complex numbers
67374
Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
6385
Minimal counterexamples of the isomorphism problem for integral group rings
61084
Examples of non-isomorphic fields with isomorphic group of units and additive group structure
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
18160
How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
45958
Proof that the Euler characteristic is additive
126513
Automorphism of the group of rational numbers under addition
119160
Isomorphism between complex numbers minus zero and unit circle
47914
Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
98507
$\text{Aut}(F)$ is isomorphic to the multiplicative group of all $n\times n$ matrices over $\mathbb Z$
99538
Non-trivial groups pairwise non-isomorphic with isomorphic direct products
152603
Group isomorphic to its automorphism group
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
147574
Prove of a finite cyclic group of order $n$ is isomorphic tto $(\mathbb Z_n,+)$.
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
94090
How to show that for any abelian group $G$, $\text{Hom}(\mathbb{Z},G)$ is isomorphic to $G$
5996
Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?