$(\mathbb{Q},+)$ isn't direct product of two non-trivial groups
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
129120
Example of a group $G$ such that $G = N_1\cdots N_n$ and $N_i \cap N_j = \{e\}$ for all $i \neq j$ but $G$ is not the internal direct product of them.
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
80849
There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
23077
Prove that the dihedral group $D_4$ can not be written as a direct product of two groups
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
99538
Non-trivial groups pairwise non-isomorphic with isomorphic direct products
113259
The confusing nature of direct sum for finite abelian groups
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
87534
Finitely generated group which is not finitely presented
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center