Is there an example of a group G and an infinite subset H of G that is not a subgroup of G?
124732
Finding a nonempty subset that is not a subgroup
122353
Status of the classification of non-finitely generated abelian groups.
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
47937
Example of a Borel set that is neither $F_\sigma$ nor $G_\delta$
150207
Non isomorphic subgroups of cyclic groups
151130
When is the product of $n$ subgroups a subgroup?
10816
Infinitely generated subgroup of a finitely one (weird)
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
156941
Subgroups of $\mathbb{Z}$
91021
Torsion elements of a group aren't necessarily a subgroup
24181
Showing that $G$ is a group under an alternative operation.
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
157841
Existence of a non-abelian group of order $p^n$.
6189
Examples of infinite groups such that all their respective elements are of finite order.
139611
Can a normal subgroup of a finite nonabelian group be nonabelian?
89749
Example of a not recursively enumerable set $A \subseteq \mathbb{N}$
129452
Groups $G,H$ with surjective homomorphisms that are quotient of each other