Does there exists a finite index non-trivial subgroup of $\mathbb{C}^*$
95867
Subgroup of $C^*$ (nonzero complex) with finite index.
151210
How can we find and categorize the subgroups of $\mathbb{R}$?
47539
Find an abelian infinite group such that every proper subgroup is finite
98474
Show the existence of a certain subgroup of F2
102912
Subgroups of finitely generated groups are not necessarily finitely generated
150207
Non isomorphic subgroups of cyclic groups
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
156941
Subgroups of $\mathbb{Z}$
58937
Finite Index of Subgroup of Subgroup
46001
Can a finite group act freely (as homeomorphisms) on $\mathbb R^n$
151619
A finite abelian group containing a non-trivial subgroup which lies in every non-trivial subgroup is cyclic
6115
Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
84869
Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
7640
Exactly one nontrivial proper subgroup
99114
Subgroups of index 3 are normal
46121
Does the intersection of two finite index subgroups have finite index?