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A Z-group is a (finite) group all of whose Sylow subgroups are cyclic. Such groups are metacyclic, supersolvable and monomial.

Every cyclic group is a Z-group, but the converse does not hold, as shown by these examples.

Knowl status:
  • Review status: reviewed
  • Last edited by David Roe on 2021-10-08 14:10:21
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