Noetherian group

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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This is a variation of finiteness (groups)|Find other variations of finiteness (groups) |

Definition

Symbol-free definition

A group is said to be slender or Noetherian or to satisfy the maximum condition on subgroups if it satisfies the following equivalent conditions:

• Every subgroup is finitely generated
• Any ascending chain of subgroups stabilizes after a finite length

Formalisms

In terms of the hereditarily operator

This property is obtained by applying the hereditarily operator to the property: finitely generated group
View other properties obtained by applying the hereditarily operator

Relation with other properties

Stronger properties

• Finite group

Weaker properties

• Finitely generated group
• Maximal-covering group