# Group satisfying descending chain condition on normal subgroups

## Definition

A group is termed a **group satisfying descending chain condition on normal subgroups** if any descending chain condition on normal subgroups stabilizes after a finite length.

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

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Artinian group |