Class two normal subgroup
This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): group of nilpotence class two
View a complete list of such conjunctions
Definition
A subgroup of a group is termed a class two normal subgroup if it is a normal subgroup and is also nilpotent, with nilpotence class at most two.
Examples
VIEW: subgroups satisfying this property | subgroups dissatisfying property normal subgroup | subgroups dissatisfying property group of nilpotency class two
VIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions
Relation with other properties
Stronger properties
- Abelian normal subgroup
- Central subgroup
- Critical subgroup
- Class two characteristic subgroup
- Commutator-in-center subgroup
- Aut-abelian normal subgroup