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## 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]