Noetherian group: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Finite group]] | * [[Weaker than::Finite group]] | ||
* [[Weaker than::Finitely generated Abelian group]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
* [[Finitely generated group]] | * [[Stronger than::Finitely generated group]] | ||
* [[Maximal-covering group]] | * [[Stronger than::Maximal-covering group]] | ||
Revision as of 13:46, 2 July 2008
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
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