Show that $S_n$ is never isomorphic to a subgroup of $A_{n+1}$ for $n\ge 2$
131594
Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
151862
Is any subgroup of a direct product isomorphic to a direct product of subgroups?
139451
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
108691
Characterize the natural numbers $n$ such that there is a surjective group homomorphism from $S_n$ to $S_{n-1}$.
99538
Non-trivial groups pairwise non-isomorphic with isomorphic direct products
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
113925
Normal Subgroup Counterexample
152662
Proving that any finite cyclic group of order $n$ is isomorphic to $$
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
144788
Cosets of a subgroup do not overlap
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.