This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Relation with other properties
Conjunction with other properties
- Central subgroup: An Abelian subgroup that is also a central factor.
- Abelian normal subgroup: An Abelian subgroup that is also a normal subgroup.
- Abelian characteristic subgroup: An Abelian subgroup that is also a characteristic subgroup.
- Maximal among Abelian subgroups: An Abelian subgroup that is also a self-centralizing subgroup.
This subgroup property is left-hereditary: any subgroup of a subgroup with this property also has this property. Hence, it is also a transitive subgroup property.
This subgroup property is not join-closed, viz., it is not true that a join of subgroups with this property must have this property.
Read an article on methods to prove that a subgroup property is not join-closed