Solvable 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): solvable group
View a complete list of such conjunctions

Definition

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

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

Relation with other properties

Stronger properties

• Abelian characteristic subgroup
• Nilpotent characteristic subgroup

Weaker properties

• Solvable normal subgroup