Need help with proving that group is not finitely-generated
32516
show that rational numbers with the multipiciation are not abelian finitely generated group
122353
Status of the classification of non-finitely generated abelian groups.
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
92298
The additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group
114522
Prove that identity is unique in a group
29717
Not sure how to go about this group theory proof
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
121141
Proving Finiteness of Group from Presentation
131306
Prove that a group of order $2^5 \cdot 7^5$ is not simple
131516
Subgroup generated by n-th powers of elements
76504
Non-trivial cyclic group with unique generator
58076
Subgroup generated by a set
126089
Showing $U(20)$ is not cyclic: Is my proof correct?
126771
Group element not taken to its inverse by any automorphism
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
85222
Direct sum of finitely-many non-abelian groups