$\mathbf{A_4}\oplus\mathbf{Z_3}$ has no subgroup of order $18$.
132816
$A_4 \oplus Z_3$ has no subgroup of order 18
106577
If G is not abelian with order $p^3$ then $G'=Z(G)$
33338
Problem on $\operatorname{Hom}(\mathbb Z_6,R^*\oplus C^*)$
112880
There are no semisimple Lie algebras of dimension $4$, $5$, or $7$
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
85677
Is there a free subgroup of rank 3 in $SO_3$?
68672
Commutator subgroup of rank-2 free group is not finitely generated.
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
99309
Groups of order $n^2$ that have no subgroup of order $n$
129830
A group with no proper non-trivial subgroups
3439
Other proofs that subgroups of $A_5$ have order at most 12
156549
Prove that there is no group $G$ s.t. $\operatorname{Aut}(G)=\mathbb{Q}$
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
136917
Torsion elements do not form a submodule.
11731
Normal subgroups of $S_4$
74586
Prove that every group of order $4$ is abelian