# Locally Noetherian group

From Groupprops

## Definition

A **locally Noetherian group** is a group satisfying the following equivalent conditions:

- Every finitely generated subgroup is a Noetherian group.
- Every subgroup of a finitely generated group is a finitely generated group.

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 |
---|---|---|---|---|

abelian group | ||||

nilpotent group |