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Metacyclic group

From Wikipedia, the free encyclopedia

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

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Metacyclic groups are both supersolvable and metabelian.

Examples

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References

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