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Proposition: Group Homomorphisms with Cyclic Groups

Let \((G,\ast)\) be any group under the operation "\(\ast\)" and let \((\mathbb Z,+)\) be the group of all integers under the operation "\(+\)" (addition). \(G\) is cyclic, if and only if there is a surjective group homomorphism \(f:\mathbb Z\mapsto G\).

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Proofs: 1

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References

Bibliography

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