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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 $n\in\mathbb N.$

Table of Contents

Proofs: 1

Mentioned in:

Explanations: 1
Proofs: 2 3
Theorems: 4 5

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References

Bibliography

  1. Modler, Florian; Kreh, Martin: "Tutorium Algebra", Springer Spektrum, 2013