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Theorem: Classification of Cyclic Groups

Let $(G,\ast)$ be a cyclic group. Then $G$ is isomorphic: * either to the group of integers, together with addition $(\mathbb Z,+),$ if $G$ is of infinite order $|G|=\infty,$ * or to the additive subgroup of integers $(\mathbb Z_n,+),$ if $|G|=n.$

Table of Contents

Proofs: 1

1. Definition: Group Order

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Explanations: 1
Proofs: 2

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References

Bibliography

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