Prove that $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic as groups
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
150207
Non isomorphic subgroups of cyclic groups
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
124864
A not free $\mathbb{Z}$-module
5996
Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
116594
Finite fields are isomorphic
18160
How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
116707
Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
118073
Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
84869
Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
5906
All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
87160
Prove $\mathbb{Z}_3[x]/(x^2+1)$ and $\mathbb{Z}_3[x]/(x^2+x-1)$ are isomorphic.