# Group whose center is normality-large

From Groupprops

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 propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Contents

## Definition

A **group whose center is normality-large** is a group such that the intersection of its center with any nontrivial normal subgroup is nontrivial.

## Relation with other properties

### Stronger properties

- Abelian group
- Nilpotent group
- Quasisimple group that is not simple (i.e., a perfect group with a nontrivial center, such that the quotient by the center is a simple group)