Class two characteristic subgroup
From Groupprops
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
Contents
Definition
A subgroup of a group is termed a class two characteristic subgroup 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.
Examples
VIEW: subgroups satisfying this property | subgroups dissatisfying property characteristic 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 characteristic subgroup
- Cyclic characteristic subgroup
- Critical subgroup
- Aut-abelian characteristic subgroup
