Metacyclic group

In group theory, a metacyclic group is an extension of a cyclic group by a cyclic group. That is, it is a group G for which there is a short exact sequence

where H and K are cyclic. Equivalently, a metacyclic group is a group G having a cyclic normal subgroup N, such that the quotient G/N is also cyclic.

Properties

Metacyclic groups are both supersolvable and metabelian.

Examples

References

  • A. L. Shmel'kin (2001) [1994], "Metacyclic group", Encyclopedia of Mathematics, EMS Press


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.