Artinian group
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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) |
Contents
Definition
A group is said to be Artinian or to satisfy the minimum condition on subgroups if every descending chain of subgroups stabilizes after a finite stage.
Relation with other properties
Stronger properties
Weaker properties
- Periodic group: For proof of the implication, refer Artinian implies periodic and for proof of its strictness (i.e. the reverse implication being false) refer Periodic not implies Artinian.
- Co-Hopfian group: For proof of the implication, refer Artinian implies co-Hopfian and for proof of its strictness (i.e. the reverse implication being false) refer Co-Hopfian not implies Artinian.
- Minimax group
