Nilpotent 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): nilpotent group
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a nilpotent characteristic subgroup if it is characteristic as a subgroup and nilpotent as a group.

For a finite group, this is equivalent to being a characteristic subgroup contained inside the Fitting subgroup.

Relation with other properties

Stronger properties

• Abelian characteristic subgroup

Weaker properties

• Nilpotent normal subgroup
• Solvable characteristic subgroup
• Solvable normal subgroup