Class two characteristic subgroup

This article describes a property that arises as the conjunction of a subgroup property: characteristic subgroup with a group property (itself viewed as a subgroup property): group of nilpotency class two
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a class two characteristic two if it is a group of nilpotency class two and is a characteristic subgroup of the whole group.

Note that group of nilpotency class two means group whose nilpotency class at most two, so this includes abelian characteristic subgroups.

Relation with other properties

Stronger properties

• Abelian characteristic subgroup
• Cyclic characteristic subgroup
• Critical subgroup
• Aut-abelian characteristic subgroup

Weaker properties

• Class two normal subgroup
• Nilpotent characteristic subgroup