Cyclic-center group

From Groupprops
Jump to: navigation, search
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions


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

Weaker properties