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- Any cyclic group is metacyclic.
- The direct product or semidirect product of two cyclic groups is metacyclic. These include the dihedral groups, the quasidihedral groups, and the dicyclic groups.
- Every finite group of squarefree order is metacyclic.
- More generally every Z-group is metacyclic. A Z-group is a group whose Sylow subgroups are cyclic.
- A. L. Shmel'kin (2001), "Metacyclic group", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
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