Cyclic-center 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 group is said to be a cyclic-center group if its center is a cyclic group.

Definition with symbols

A group $G$ is said to be a cyclic-center group if there is $x\in G$ such that $Z(G)=<x>$.

Relation with other properties

Stronger properties

• Centerless group
• Cyclic group
• Simple group
• Linearly primitive group