Metacyclic group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

Symbol-free definition

A metacyclic group is a group having a cyclic normal subgroup with a cyclic quotient group.

Definition with symbols

A group $G$ is termed metacyclic if there exists a normal subgroup $N$ of $G$ such that both $N$ and $G/N$ are cyclic.

Relation with other properties

Stronger properties

• Cyclic group

Weaker properties

• Supersolvable group
• Polycyclic group
• Metabelian group
• Solvable group

Facts

• Classification of metacyclic p-groups