# Group whose center is comparable with all normal subgroups

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A group whose center is comparable with all normal subgroups is defined as a group whose center is a subgroup comparable with all normal subgroups. In other words, every normal subgroup is either a central subgroup (i.e., it is contained in the center) or is a subgroup containing the center.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Normal-comparable group any two normal subgroups are comparable center is normal |FULL LIST, MORE INFO