Metacyclic group

Last updated

In group theory, a metacyclic group is an extension of a cyclic group by a cyclic group. Equivalently, a metacyclic group is a group having a cyclic normal subgroup , such that the quotient is also cyclic.

Contents

Metacyclic groups are metabelian and supersolvable. In particular, they are solvable.

Definition

A group is metacyclic if it has a normal subgroup such that and are both cyclic. [1]

Examples

References

  1. Kida, Masanari (2012). "On metacyclic extensions". Journal de Théorie des Nombres de Bordeaux. 24 (2): 339–353. ISSN   1246-7405.