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

Weaker properties

• Nilpotent normal subgroup