Complete 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): complete group
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a complete characteristic subgroup or complete characteristic direct factor if it satisfies the following equivalent conditions:

1. It is complete as a group and is a characteristic subgroup of the whole group.
2. It is complete as a group and is a characteristic direct factor of the whole group.

Relation with other properties

Weaker properties

• Characteristic direct factor
• Complete direct factor
• Direct factor
• Characteristic subgroup
• Normal subgroup