Why is $(\mathbb{Q}, \cdot )$ not a group?
2458
Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why?
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
42213
Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
23077
Prove that the dihedral group $D_4$ can not be written as a direct product of two groups
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
55393
Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
92493
If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$
51196
A group of order $p^2q^2$ is never simple
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
152297
Understanding quotients of $\mathbb{Q}[x]$
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
98507
$\text{Aut}(F)$ is isomorphic to the multiplicative group of all $n\times n$ matrices over $\mathbb Z$
157496
Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$
32516
show that rational numbers with the multipiciation are not abelian finitely generated group
86234
Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field