Proposition: Additive Subgroups of Integers 

The subgroups of the additive group $(\mathbb Z, +)$ are exactly the groups $(S_n, +)$ of the form $S_n=n\mathbb Z:=\{nx\mid x\in\mathbb Z\}$ for all natural numbers $n\in\mathbb N.$

| | | | | created: 2019-07-28 13:39:48 | modified: 2019-08-03 10:31:38 | by: bookofproofs | references: [677]

1.Proof: (related to "Additive Subgroups of Integers")