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

gollark: Well, it won't ping me with my reminders for a week.
gollark: Yes. You pinged me, thus I was pinged.
gollark: ++remind 1w \<@160279332454006795>
gollark: ++remind 1mo <@!160279332454006795>
gollark: ++help

References

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


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