Metacyclic group

Template:Short description In group theory, a metacyclic group is an extension of a cyclic group by a cyclic group. Equivalently, a metacyclic group is a group $G$ having a cyclic normal subgroup $N$, such that the quotient $G/N$ is also cyclic.

Definition

A group $G$ is metacyclic is there is a normal subgroup $N$ such that the sequence below is exact:

$1\to N\to G\to G/N\to 1,$

References

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