Prove or disprove: Every subgroup of the integers has finite index.
106660
Every subgroup of the integers has finite index
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
156941
Subgroups of $\mathbb{Z}$
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
144218
Does every finite nilpotent group occur as a Frattini subgroup?
46121
Does the intersection of two finite index subgroups have finite index?
81354
The product of all the elements of a finite abelian group
45792
Rigorous proof that surjectivity implies injectivity for finite sets
58694
Which non-abelian finite groups have the property that every subgroup is normal?
58863
Proof that $A_n$ the only subgroup of $ S_n$ index $2$.
58937
Finite Index of Subgroup of Subgroup
35602
If a subgroup has smallest prime index, then it is normal
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
103717
Topological Property of the Set of Integers
144582
Index of a subgroup in $SL_2(\mathbb{Z})$
145563
In an abelian group, the elements of finite order form a subgroup.
51359
Prove that every subgroup of an abelian group is a normal subgroup.