Noetherian group

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


 * 1) Every subgroup is finitely generated
 * 2) Any ascending chain of subgroups stabilizes after a finite length.
 * 3) Any nonempty collection of subgroups has a maximal element: a member of that collection that is not contained in any other member of the collection.