Noetherian group: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[group]] is said to be '''slender''' or '''Noetherian''' if it satisfies the following equivalent conditions: | 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 group|finitely generated]] | * Every [[subgroup]] is [[finitely generated group|finitely generated]] | ||
Revision as of 21:33, 10 December 2007
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