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Lemma: Subgroups of Cyclic Groups
Let \((G,\ast)\) be a cyclic group and \(H\subseteq G\) its subgroup. Then \(H\) is again cyclic. In other words, each subgroup of a cyclic group is a cyclic group.
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Proofs: 1 2
- Modler, Florian; Kreh, Martin: "Tutorium Algebra", Springer Spektrum, 2013