Slender group
From Wikipedia, the free encyclopedia
In mathematics, in the realm of group theory, a group is said to be slender or Noetherian if every subgroup of it is finitely generated. Some facts about slender groups: Equivalently the group satisfies the ascending chain condition on subgroups, that is, every ascending chain of subgroups stabilizes after a finite stage.
- Every finite group is slender.
- Every subgroup of a slender group is slender.
- In a slender group, every subgroup is contained in a maximal subgroup.
