Does there exist an infinite non-abelian group, such that all its nontrivial proper subgroups are isomorphic to $C_\infty$?
9232
Group with proper subgroups infinite cyclic
80849
There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$)
13924
For all infinite cardinals $\kappa, \ (\kappa \times \kappa, <_{cw}) \cong (\kappa, \in).$
102079
If $1\leq p < \infty$ then show that $L^p([0,1])$ and $\ell_p$ are not topologically isomorphic
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
92298
The additive group $\mathbb{G}_a$ over an infinite field $k$ is not a topological group
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
42582
Infinite group with only two conjugacy classes
85222
Direct sum of finitely-many non-abelian groups
112993
Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
30825
Infinite coproduct of abelian groups
123677
Normal subgroups of infinite symmetric group
153921
Infinite nilpotent group, any normal subgroup intersects the center nontrivially
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
121481
Non-abelian finite $p$-group in which every element has prime order?
35353
Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?
58694
Which non-abelian finite groups have the property that every subgroup is normal?