Additive group of all polynomials in x with integral coefficients is isomorphic to $\mathbb{Q}^*$
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
90433
Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
152297
Understanding quotients of $\mathbb{Q}[x]$
41846
$(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$
29359
Localisation isomorphic to a quotient of polynomial ring
30236
isomorphic groups related in direct product.
145561
About the additive group and the multiplicative group of a field
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
85752
Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
6385
Minimal counterexamples of the isomorphism problem for integral group rings
87160
Prove $\mathbb{Z}_3[x]/(x^2+1)$ and $\mathbb{Z}_3[x]/(x^2+x-1)$ are isomorphic.
155575
Proving a polynomial $f(x)$ composite for infinitely many $x$
108156
Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
42810
Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group