Locally Noetherian group

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Definition

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

  1. Every finitely generated subgroup is a Noetherian group.
  2. 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 properties
VIEW 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