Cyclic-center group

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 $$Z(G) = $$.

Stronger properties

 * Centerless group
 * Cyclic group
 * Simple group
 * Linearly primitive group