Group satisfying ascending chain condition on subnormal subgroups
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A group is said to satisfy the ascending chain condition on subnormal subgroups or the maximum condition on subnormal subgroups if it satisfies the following equivalent conditions:
- Any ascending chain of subnormal subgroups stabilizes after a finite length.
- Any nonempty collection of subnormal subgroups has a maximal element: a member that is not contained in any other member of the collection.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Noetherian group|||FULL LIST, MORE INFO|
|group of finite composition length|||FULL LIST, MORE INFO|
|simple group|||FULL LIST, MORE INFO|